Electronic copy available at: http://ssrn.com/abstract=1935011
The Indirect Impact of Price Deals on Households’ Purchase Decisions
Through the Formation of Expected Future Prices
Assistant Professor of Marketing, University of Iowa
W. Patrick McGinnis Professor of Marketing, Washington University in St. Louis
Philip L. Siteman Professor of Marketing, Washington University in St. Louis
† Corresponding Author: P.B. Seetharaman, email: Seethu@wustl.edu; Ph: 314-935-3574.
Electronic copy available at: http://ssrn.com/abstract=1935011
We examine the indirect impact of price deals, which occurs through the formation of
expected future prices, on households’ purchase decisions. Two competing learning processes of
households’ formation of expected future deals that lead to opposite predictions are proposed.
Under a deal-probability learning process, a current deal on a brand raises households’
expectations of a deal on the same brand in the immediate future, while under a deal-timing
learning process, a current deal on a brand lowers households’ expectations of a deal on the
same brand. We embed each learning specification within a comprehensive econometric
framework that simultaneously examines three purchase decisions – incidence, brand choice and
quantity – at the household level, while explicitly correcting for two sources of selectivity bias in
discrete quantity outcomes. We estimate the proposed model using scanner panel data on paper
towels, and find that (1) the deal-probability learning process better describes how households
incorporate the deal information into the formation of future price expectations compared to the
deal-timing learning process; (2) the indirect impact of price deals is greater for brand-loyals
than for brand-switchers; and (3) the indirect impact of price deals is greater for larger families,
heavy users, less educated and less employed households, and infrequent shoppers. We also
show that ignoring the indirect impact of price deals severely overstates the sales effects.
Keywords: Consumer Learning, Price Deals, Direct and Indirect Deal Effects, Discrete Quantity
Model, Self-Selectivity Correction.
Deal (i.e., discounted) prices are known to affect consumers’ purchase behavior directly –
as extensively documented by marketing researchers using scanner panel data – so do consumers’
future price expectations (e.g., Gonul and Srinivasan 1996, Erdem, Imai and Keane 2003, Sun
2005, Chan, Narasimhan and Zhang 2008). However, whether and how today’s price deals affect
the formation of expected future prices have been relatively understudied in Marketing. For
example, when a deal price is observed on a brand during a shopping trip, a consumer may make
one of the following (opposite) inferences: either the deal price will likely reappear in the
immediate future; or the deal price will be retracted following the current period and reappear
several periods later. Consequently, the two different inferences will have opposite implications
on the consumer’s current purchase behavior – if the consumer infers the future brand price to
continue to be low, it decreases the attractiveness of the current deal and, therefore, the consumer
will purchase later, will purchase a smaller quantity than otherwise, or both; on the other hand, if
the consumer infers the future price to be higher, it increases the attractiveness of the current deal
and therefore, the consumer will purchase sooner, will purchase a larger quantity than otherwise,
or both (Talukdar, Gauri and Grewal 2010). We call this the indirect impact of price deals on
consumers’ purchase decisions.
Understanding the indirect impact of price deals on consumers’ purchase decisions is
important for manufacturers and retailers, as it affects the evaluations of the effectiveness of their
deal strategies (Moreau, Krishna and Harlem 2001). For example, if a current deal price is
associated with lower future prices, the effectiveness of the price deal in stimulating consumers
to purchase earlier or more will be less than in the case if a current deal price is associated with
higher future prices. The indirect impact may be different for consumers with different
characteristics (e.g., demographic and behavioral) and different degrees of attachment with
brands (e.g., brand-loyals vs. brand-switchers). Brand-loyals, especially those with a consistent
consumption rate, are more likely to adopt a process that assures them of a steady supply of their
favorite brand. Brand-switchers, and especially those who are less frequently in the market, are
likely to adopt an expectation process that lets them use multiple brands by adjusting their
consumption schedule. Understanding such heterogeneity will have important implications for
differentiated deal strategies that aim to target different consumer groups (Magi and Julander
In light of this, we propose the following research questions that motivate this research:
(1) how do price deals affect consumers’ purchase decisions through the formation process of
expected future prices? (2) how do the effects differ across different consumer groups? Both
questions address the issue of how consumers behaviorally respond to price changes over time,
which, among four issues, has been recently identified as holding the potential for the greatest
contribution in the future for retailing research (Grewal and Levy 2009).
In studying the above-mentioned questions, we take the view that consumers’
expectations of future prices are adaptive, i.e., consumers update their expectations based on the
historical observations of brand prices. In contrast to the rational expectations view that assumes
that consumers form unbiased expectations of brands’ future prices based on a full understanding
of the underlying market process determined by the firm, the adaptive expectations view does
not assume consumers to have perfect knowledge of brands’ future prices but allows them to
learn about a brand’s pricing patterns using historical data. Such a view is consistent with the
bounded rationality approach that is gaining advocacy in marketing models of consumer and
firm behavior (Mehta, Rajiv and Srinivasan 2004, Che, Sudhir and Seetharaman 2007).
In the adaptive price expectations approach that we employ in this paper, consumers are
assumed to be certain about the deal price and regular price of a brand, but uncertain about the
temporal occurrence of a deal in a given future period, for which they form expectations about
the probability. We use two learning models – deal-probability learning and deal-timing learning
– to respectively capture two types of expectations in which the observation of a deal price for a
brand will result in opposite inferences by consumers: either the deal price will likely reappear in
the immediate future; or the deal price will be retracted following the current period and reappear
several periods later. In the deal-probability learning process, consumers engage in a Bayesian
updating on the probability that a brand will be on a deal, and in deal-timing learning process,
consumers undertake a Bayesian updating on the time intervals between deals. We will explain
the two learning processes in more detail in the modeling section.
We examine the above-mentioned learning processes, one at a time, within a
comprehensive econometric model of purchase incidence, brand choice and purchase quantity
decisions of consumers. When modeling the three purchase decisions simultaneously, one
technical concern that arises in the estimation context is the fact that a consumer’s quantity
decision may be correlated, for unobserved reasons, with the consumer’s incidence and brand
choice decisions. For example, suppose a consumer buys the product at a shopping occasion for
unobserved reasons – such as the unexpected arrival of guests at home – that are not explicitly
accounted for by the covariates in the incidence model. In such a case, the consumer may also be
likely to buy a larger quantity of the product for the same unobserved reasons. Similarly, the
consumer may buy a specific brand of the product and also a larger quantity for the same
unobserved reasons. Unless such correlations in unobservables are accommodated, the parameter
estimates in incidence, brand choice and quantity models may be biased. Such unobserved
correlations, also called endogenous self-selectivity, have been accommodated in previously
proposed models (e.g., Chiang 1991). However, the technique does not apply when the quantity
model is discrete, as in our case. Therefore, we adopt an econometric technique that is
appropriate for correcting the selectivity bias in the observed discrete quantity outcomes (Zhang,
Seetharaman and Narasimhan 2005).
We estimate the proposed models using an IRI scanner panel dataset on household
purchases in the paper towel category in a large U.S. metropolitan market. The dataset spans the
period from June 1991 to June 1993. We find that (1) the deal-probability learning process better
describes how households incorporate the deal information into the formation of future price
expectations compared to the deal-timing learning process; (2) the indirect impact of price deals
is greater for brand-loyals than for brand-switchers; and (3) the indirect impact of price deals is
greater for larger families, heavy users, less educated and less employed households, and
infrequent shoppers. We run a policy simulation to demonstrate how ignoring the indirect impact
of price deals would lead to an overstatement of the predicted sales in a holdout sample. We also
document the importance of correcting the endogenous self-selectivity in the econometric model
that arises due to correlations among three purchasing outcomes.
The rest of the paper is organized as follows. In the next section we discuss the pertinent
previous literature and position our work relative to this literature. Next, we develop our
specifications of two alternative learning processes. In the model section, we propose a
comprehensive econometric model of purchase incidence, brand choice and purchase quantity. In
the following two sections, we describe the data and discuss the main results, respectively.
Finally, we conclude with opportunities for future research.
Previous empirical research has established that price deals have direct/immediate impact
on consumers’ purchasing behavior. This manifests in three ways: (1) purchase incidence
acceleration of the promoted brand (e.g., Gupta 1988, Chiang 1991, Bucklin and Gupta 1992,
Chintagunta 1993, Seetharaman 2004a), (2) brand switching toward the promoted brand (e.g.,
Guadagni and Little 1983, Gupta 1988, Krishnamurthi and Raj 1988, Chiang 1991, Chintagunta
1993, Seetharaman 2004b), and (3) increased purchase quantities of the promoted brand
(Krishnamurthi and Raj 1988, Chiang 1991, Chintagunta 1993).
Besides the direct impact of price deals, consumers’ expectations about future marketing
variables (e.g., coupons, quality etc.) have been shown to have an impact on consumers’
purchasing and consumption decisions. With regard to expected future prices, Winer (1986) and
Bridges, Yim and Briesch (1995) document such effects for durable goods, while Gonul and
Srinivasan (1996), Erdem, Imai and Keane (2003), Sun (2005), Hendel and Nevo (2006), and
Chan, Narasimhan and Zhang (2008) document such effects for non-durable goods. Rust, Inman,
Jia and Zahorik (1999) document the effects of expected future quality.
Two types of models that describe consumers’ formation process of future price
expectations – (1) rational expectations, and (2) adaptive expectations - are popular in the
literature. Several empirical studies have incorporated the rational expectations process within
models of consumer purchasing behavior (e.g., Krishna 1992, 1994a, Gonul and Srinivasan 1996,
Erdem, Imai and Keane 2003, Sun 2005, Erdem, Katz, and Sun 2010). The rational expectations
models have high information requirements that consumers have a full understanding of the
underlying price process that is determined by manufacturers or retailers, which is often
unrealistic in the actual purchase situation (Lovell 1986). Furthermore, previous research has
shown that models with adaptive expectations generally outperform rational expectations models
on actual data (Chow 1989, Johnson, Anderson and Fornell 1990). In our study, therefore, we
take the view that consumers form adaptive expectations. Further, we empirically test two
alternative forms of adaptive expectations on price deals.
Alternative adaptive price expectations processes have been tested in the reference prices
literature. This literature, starting with Winer (1986), defines consumers’ price expectations,
using the construct of reference prices, within brand choice models (e.g., Mayhew and Winer
1992, Hardie, Johnson and Fader 1993, Han, Gupta and Lehmann 2001, Moon, Russell and
Duvvuri 2006). Lattin and Bucklin (1989) extend Winer’s (1986) framework to estimate
reference promotion effects in consumers’ brand choices. These studies have conceptualized
reference prices as backward looking constructs in the sense of being functions of past prices.
Winer (1986) and Jacobson and Obermiller (1990), on the other hand, argue that expected future
prices of brands could also serve as reference prices to consumers, and that such reference prices
would be functions of not only past prices but also current prices of brands. In line with this view,
in this paper, we explicitly model the process by which consumers combine not only past but
also current deal information of brands to form expectations on future deals.
In this paper, we adopt the econometric approach of Chiang (1991), Chintagunta (1993)
and Arora, Allenby and Ginter (1998) to model three household-level purchase decisions -
purchase incidence, brand choice, and purchase quantity - simultaneously for consumer
packaged goods, but with two modifications. One, we assume consumers to be forward-looking
and embed their expectations on future deals into the unified econometric model. In doing this,
we separately account for direct and indirect effects of price deals on consumers’ purchase
decisions. Two, as the quantity outcomes in our model are discrete, we correct the selectivity
bias in the observed discrete quantity outcomes using the technique proposed by Zhang,
Seetharaman and Narasimhan (2005).
FUTURE PRICE EXPECTATIONS
We describe how a household forms expectations about a brand’s future price at any
given period in a frequently purchased product category. We will use the subscript j for a brand,
and t for a shopping trip. The formation processes of households’ future price expectations are
based on the following assumptions: 1) households expect the price of a brand in each future
period to be either a deal price or a regular price; 2) households know both a brand’s deal price
and regular price with certainty but are uncertain about the likelihood that a deal will occur in a
given future period.
Previous research on assimilation-contrast theory (Sawyer and Dickson 1984,
Kalyanaram and Little 1994) shows that consumers have subjective latitudes of prices. Any price
within a latitude is assimilated with other prices in that latitude. As the observed prices of brands
in our data follow a bimodal distribution, see Figure 1 as an example, we postulate that
consumers perceive that there are two such price latitudes for a brand, one for the regular price
and another for the deal price. Behavioral research has found that consumers react more strongly
to presence of a discount than to the size of the discount (Inman, McAlister and Hoyer 1990,
Mayhew and Winer 1992, Wakefield and Inman 1993, Lichtenstein, Burton and Netemeyer
1997), rationalizing our modeling consumers’ uncertainty about deal occurrences, rather than
[Insert Figure 1 Here]
We use an indicator variable,
, j tm
, to denote whether or not a deal occurs on brand j at
shopping trip t + m, m = 1, 2, ...,. This variable takes the value 1 if a deal occurs on brand j at trip
t + m, and 0 otherwise. We use Prjtm
to denote the probability of deal occurrence on brand j at
trip t + m. This probability is determined by the manufacturer of brand j or the retailer (in this
model, we do not distinguish between these two decision makers), and is unobserved by a given
household h. Household h, however, “learns” about this probability on the basis of the values of
that the household has observed in its past and current shopping trips. We use the
to denote household h’s expectation of Prjtm
. Given this expectation about deal
occurrence, at trip t, the household expects the future price of brand j for trip t + m, m=1, 2,…,
, to be as follows:
hjtm hjtm jd hjtm jr
P stand for the deal price and regular price of brand j respectively.1
When household h observes a deal on brand j at trip t, the household makes one of two
inferences based on the observation: either it indicates that the probability of deal occurrence at
the next trip will increase or it is regarded as a “turning point” for temporal occurrence of deal on
the brand, and therefore the household will expect a lower probability of deal occurrence at the
next trip. We propose two alternative learning processes – (1) deal-probability learning, and (2)
deal-timing learning – to capture how household h learns about the expected future probability of
deal occurrence on brand j (i.e.,
), which respectively accommodate the two different
effects described above. We compare the empirical performance of these two alternative learning
1 In our empirical analysis, the two price latitudes,
and regular prices of brand j respectively (Sawyer and Dickson 1984).
P are constructed by using the means of observed deal
processes that are embedded in a unified decision model using scanner panel data, in order to
understand which effect seems to characterize observed purchase behavior of households in data.
Deal-probability Learning Process
Under the deal-probability learning process, a household holds a prior belief about the
probability that a deal occurs, and on each shopping trip updates this belief based on its
observations of deal occurrences in its past and current trips. Consider that for any t, whether
brand j is on deal or not, i.e.,
= 1 or 0, is assumed to be a binary outcome from a Bernoulli
distribution with parameter Prjt that is unknown to the household.2 Household h undertakes a
Bayesian updating process to learn about Prjt. We assume that the household’s prior knowledge
of Prjtfollows a Beta distribution.3 The posterior Beta distribution can be written as follows.
| Pr Pr|,
| PrPr|, Pr
hjt hjt hjthjthjt hjt
where P(.) is the probability mass function of the Bernoulli distribution with parameter Prhjt, and
is the density function of the Beta distribution with parameters
. The mean of
the posterior Beta distribution,
, which is the outcome of the Bayesian update, represents
the learning of the household on Prjt. It is given by
hjt hj hj hjhjt
2 We have introduced a household subscript for
the household’s shopping trips.
3 The prior distribution is assumed to be a Beta distribution for two reasons: 1) the Beta distribution is flexible and
can accommodate a wide range of shapes; 2) the Beta distribution is conjugate to Bernoulli distribution.
since observed deal outcomes for a household are conditional on
represent the prior parameters of the Beta distribution at t =1. Once this
Bayesian update happens, the household assumes that
hj tm hjt
, for all m > 0, i.e., the
Bernoulli probability of a deal occurring on brand j during any future shopping trip t is the same
for all future shopping trips.
While this Beta-Bernoulli updating process seems to be an appealing way of thinking
about how households update their expectations about deal arrivals, it is natural to think that
households may rely more on recently observed prices in learning about retail pricing policies on
brands. This may happen for two reasons: one, households have an imperfect memory for prices
observed in the distant past (Mehta, Rajiv and Srinivasan 2004); two, current pricing policies at
the store may be different from pricing policies in the distant past. For these reasons, we modify
the Beta-Bernoulli updating process to be able to handle unequal weighting of past information
on deals as shown below.
Pr Pr , for all 0,
hj hj hj
hj t mhjt
The modified specification has only an additional parameter, , which is restricted to lie
between 0 and 1, and nests the traditional Beta-Bernoulli updating process as a special case.
When = 1 it reduces to the traditional Beta-Bernoulli updating process. The larger the value of
, the more the number of previously observed deals that influence the household’s learning
about the occurrence of a deal in the next period. For this reason, we refer to as the memory
The modified Beta-Bernoulli updating process is consistent with Bayesian updating in the
following manner: suppose a household has a prior Beta distribution (with parameters
before a shopping trip t. After observing the Bernoulli outcome
at trip t, the household
engages in Bayesian updating to obtain the updated parameters,
. At the shopping trip
t , although the household still holds the same prior belief about the likelihood of deal
occurrence, the household’s uncertain about the prior information; therefore it discounts the
value (or accuracy) of the prior information by . Mathematically, this is expressed as follows.4
jt jtjt jt
jt jt jtjt
Under the deal-probability learning process, each price observation gives the household
an additional opportunity to learn about the distribution, with more recent price observations
being more relevant.
Deal-timing Learning Process
Under the deal-timing learning process, a household holds a prior belief about how long
the time interval between deals is, and in each shopping trip updates this belief based on its
observations of inter-deal times from the past and current trips. The inter-deal time for brand j is
X and we assume that (
X -1) follows a Poisson distribution with parameter
is unknown to the household. The household undertakes Bayesian updating to learn about
4 When a Beta distribution is taken as a prior for Bayesian updating, the mean,
, represents the household’s
belief about the deal probability, and
to be worth (Lee 1997).
measures the value that the household considers the prior information
We assume that the household’s prior knowledge of
follows a Gamma distribution.5 The
mean of the posterior Gamma distribution,
, which is the outcome of the Bayesian update,
represents the learning of the household on deal-timing. It can be written as shown below.
stand for the observed inter-deal times on brand j until t,
nt stands for the
total number of deals observed by the household on brand j until t,
are the prior
Gamma parameters at t = 1. Thus, given the updated
, the household’s expected probability
of deal occurrence for future periods at t follows the Poisson hazard function and can be written
is the probability mass function of the Poisson distribution with parameter
is the corresponding cumulative distribution function,
0t is the time of occurrence of the
latest deal on brand j.
Under this deal-timing learning process, each deal occurrence observation gives the
household an opportunity to learn about how long the deal interval is on average.
JOINT MODEL OF INCIDENCE, BRAND CHOICE AND QUANTITY
5 A Gamma prior distribution is assumed for two reasons: 1) the Gamma distribution is flexible and can
accommodate a wide range of shapes; 2) the Gamma distribution is conjugate to Poisson distribution.
Consider a household indexed by h (h = 1, 2, ..., H) observed over t = 1, 2, ...,
shopping occasions for a given frequently purchased product category. On each shopping
occasion, we observe a binary outcome variable
y that takes the value one if the household
made a purchase in the focal product category and zero otherwise, a multinomial outcome
y takes the value j, j = 1, 2, ..., J, if brand j is bought at that occasion, and a positive-
valued discrete outcome variable
that represents the purchase quantity for the purchase
occasion. Our goal is to model the three outcome variables (
) jointly and address two
issues – incorporating household future price expectations and correcting self-selectivity bias in
discrete quantity outcomes,
q . The details about the model estimation are given in Appendix A.
We explain the specifications for the sub-models of incidence, brand choice and quantity below.
Z denote the (indirect) utility of household h for buying the category at t.
hthh hth hth htht
CA is an inclusive value measure that captures the current attractiveness of the product
category at t and is given by (Ben-Akiva 1985)
stands for the deterministic component of household h’s indirect utility for brand k at
captures the expected future attractiveness of the product category (we will provide an
in the next sub-section titled, “Brand Choice Model”),
stands for the number of weeks for which the household h’s current stock of inventory,
will last if the household consumes the product at a constant weekly rate,
hth th t h th
, and the error term,
, is assumed to
follow the Gumbel distribution with scale parameter one.
corresponding household-specific coefficients. We expect
Under the assumption that
is distributed Gumbel with scale parameter one, this yields
the following incidence probability at the household-level.
hh hth hthht
Brand Choice Model
denote the (indirect) utility of household h for brand j on purchase occasion t be
hjhhjth hjth hjt hjt
denotes the deterministic component of the (indirect) utility,
is a brand and
household specific intercept,
PDF stand for the price, display and feature associated with
brand j at t as observed by household h and
are corresponding household-
specific coefficients. We assume that the errors
hth th t hJt
are iid Gumbel distributed
6 We do not allow these utilities to further depend on expected future prices of brands since the household’s
incentive to accelerate to decelerate purchase is already captured in the incidence model, and we do not expect
further dynamics, such as due to households’ learning about attributes, to characterize brand choices in a mature
with scale parameter one. This assumption yields the following brand choice probabilities at the
denote the deterministic component of the expected (indirect) utility of
household h for brand j at a future shopping trip t + m. Then
hj tm hjh hj tmh hj tmhhj tm
hj tmhj tm hj tm
stand for the expected price, display and feature, respectively,
associated with brand j at t + m for household h. Since in this study we focus on the impact of
households’ future price expectations, we make a simplification that
From equation (14), we construct a term (see details in Appendix B), the expected future
, which is the future counterpart of the deterministic component of the
(indirect) utility of household h for brand j at t,
incorporates household h’s
expectations of the brand utility for future periods after trip t. It is computed as shown below.
hjthjt hjd hjthjr
hjd hjh hjdh hjth hjt
hjr hjh hjrh hjth hjt
P are the deal price and regular price associated with brand j respectively, and
are display and feature at t. Depending on whether the learning process is deal-
probability learning or deal-timing learning,
is as follows (see Appendix B for the
Under deal-probability learning :
Under deal-timing learning:
where is a time discount factor which lies between 0 and 1.
denote the expected future category attractiveness. Analogous to the
CA in equation (10),
can be computed as shown below.
This is similar to the inclusive value variable in the nested logit model, except that it is based on
summing the household’s exponentiated expected future utilities (compared to current utilities)
for all brands.
Following the findings in Kalyanam and Putler (1997) that it is inefficient to assume
quantities to be perfectly divisible when they are count data in nature, we assume households’
q , to be discrete. Further, we assume that they follow a truncated (at zero)
Poisson distribution (Wedel, Desarbo, Bult and Ramaswamy 1993),7 i.e., household h’s
probability of buying
units of brand j is given by
( 1) !
is the parameter of the Poisson distribution that depends on covariates as shown below.
hjthh hjth hjth hthhh
VECA Inv InvK
Inv is household h’s average product inventory over the study period, and the remaining
variables are as explained before.
are corresponding coefficients. We
We employ IRI’s scanner panel data on household purchases in a metropolitan market in
a large U.S. city. For our analysis, we pick the category of paper towels. The dataset covers a
period of two years from June 1991 to June 1993 and contains shopping visit information on 219
panelists at a supermarket. The dataset contains information on marketing variables – price, in-
store displays and newspaper feature advertisements – at the SKU-level for each store and each
week. Paper towels in the data come in five package sizes, among which the single-roll package
size accounts for 85% of the total quantity sold and 92% of all purchase occasions. In fact, eight
out of the ten largest-selling brand-size combinations are of the single-roll type. Given the clear
dominance of the single-roll package size in this market, we focus our attention on this size only.
7 The frequency histogram of observed purchase quantities in the paper towels category in our data supports our
assumption of the truncated Poisson distribution. The figure is available from authors.
This helps us avoid two problems – price comparison across different package sizes and
operationalizing the purchase quantity variable in a common denomination of discrete units.
For the purpose of our empirical analysis, we select 112 of the 219 households according
to the following criteria: (1) at least 80% of their paper towels purchases are made within the
supermarket under study (as we are not modeling store switching behavior of households); (2) at
least 80% of their paper towel purchases are of the single-roll size type. These households made
9902 store visits over the study period, among which 1942 are associated with paper towel
purchases. We use the first 70 weeks of data as the calibration sample, and the remaining 34
weeks of data as the holdout validation sample.
There are eight brands in the paper towels category in the data: Private Label, Generic,
Bounty, Viva, Sparkle, Scott, Gala and Mardi Gras. Descriptive statistics pertaining to the brands
are provided in Table 1. Among the eight brands, the private label has the highest market share
(26.19 percent), while Gala has the lowest (5.87 percent). Scott is the highest-priced brand, while
the generic is the lowest-priced. In terms of average number of rolls purchased per purchase
occasion, Sparkle takes the lead among the eight brands (2.02 rolls).
In our empirical analysis, for store visits that involve purchase of paper towels, the
marketing variables for the chosen brands are computed based on the values of the SKUs bought
while those of the non-chosen brands are computed as share-weighted average values across all
SKUs belonging to the corresponding brands. For store visits that do not involve paper towel
purchases, the marketing variables of all brands are computed using the share-weighting
procedure. The indicator “Deal” is equal to 1 if the price is below the average price, 0 otherwise.
The regular prices and deal prices of brands are updated for each shopping visit, computed as the
averages of all previous visits. The deal frequency for each brand is also reported in Table 1.
[Insert Table 1 Here]
EMPIRICAL RESULTS AND DISCUSSIONS
We estimate the proposed model under two different specifications of the household’s
price expectations: (1) deal-probability learning, and (2) deal-timing learning, as discussed
earlier. We refer to these models as PROPOS-P and PROPOS-T respectively. We also estimate
two benchmark models, both of which are nested within the proposed models. One ignores the
effects of households’ future price expectations, which we refer to as BENCH-NF. The other
incorporates price expectations in the form of deal-probability learning but ignores the effects of
self-selectivity in the quantity outcomes, which we refer to as BENCH-NC. The goodness of fit
measures (i.e., LL, AIC, BIC8) of these models are reported in Table 2, as well as the log-
likelihood measure (LL) for the holdout sample based on the parameter estimates obtained in the
[Insert Table 2 Here]
Table 2 shows that, on the basis of fit criteria and the holdout validation measure, the
proposed model under deal-probability learning is the best-fitting model. This implies that for
paper towel purchases, when a consumer sees a current deal price for a brand, she/he expects the
deal price to persist in to the immediate future. It also shows that incorporating the effects of
future price expectations and correcting the self-selectivity in the quantity outcomes improve the
explanatory power of a joint econometric model of incidence, brand choice and quantity.
8 AIC stands for the Akaike Information Criterion: AIC = -2LL + 2k, where LL is the log-likelihood for the
estimation data and k is the number of parameters estimated by the model. BIC is the Bayes Information Criterion:
BIC = -2LL + k ln(N), where N is the number of iid observations in the data. Following Elrod and Keane (1995), we
compute BIC by letting N equal the number of households in the data.
9 In addition, we estimate another benchmark model in which consumers expect future prices to be an exponentially
smoothed average of past prices. There are 47 parameters in the model. The LL of the model is -6410.4, AIC is
12914.9 and BIC is 13042.7.
Next we discuss the estimation results obtained from the best-fitting model, PROPOS-P.
The estimation results for the incidence sub-model are given in Table 3. All the estimated
parameters are found to have the expected signs. The coefficients associated with expected future
category attractiveness are negative and significant (−1.03 and −2.51 for the two supports
respectively), while the coefficients associated with current category attractiveness are positive
and significant (2.29 and 2.98). This shows that a price cut in the current period has not only a
direct (positive) impact on current incidence probabilities, but also an indirect (negative) impact
through the formation of price expectations. It is useful to note that the magnitude of the
coefficient associated with current category attractiveness is larger than that associated with
expected future category attractiveness. This implies that the direct effect of a price reduction in
the current period – which would accelerate current incidence – is larger than the indirect effect
of the current price reduction – which would decelerate current incidence.
Comparing the estimated parameters associated with the two segments, we note that the
magnitudes of both the coefficient of current category attractiveness, as well as the coefficient of
expected future category attractiveness, are larger for segment 2 than for segment 1. This
suggests that the overall impact of price deals is larger for segment 2 than for segment 1. The
memory decay factor, , is 0.03 for the first segment, and 0.43 for the second segment. This
suggests that households belonging to the first segment account primarily for current prices only
while learning about future prices (effectively believing that the current prices will persist in to
the future). In contrast, households belonging to the second segment seem to account for not only
current prices but also past prices while learning about future prices.
[Insert Table 3 Here]
The estimation results for the brand choice sub-model are given in Table 4. The estimates
of the price and display parameters have the expected signs while the estimated feature
parameter is insignificant for both segments. In terms of the estimated brand intercepts, segment
1 is found to prefer major national brands – Bounty, Viva and Scott – compared to the other
brands. Segment 1 is also found to be more price-sensitive than segment 2.
[Inset Table 4 Here]
The estimation results for the quantity sub-model are given in Table 5. The coefficient of
the deterministic component of utility associated with the purchased brand is significant and
positive. This implies that current price reductions have a direct (positive) impact in terms of
increasing households’ purchase quantities. The coefficient of expected future category
attractiveness, however, is found to be insignificant. This suggests that there is no indirect impact
of current price reductions on current quantity decisions.
[Insert Table 5 Here]
We profile the estimated segments in terms of demographic and shopping characteristics.
In order to do this, in the maximum likelihood procedure, we allow each household’s prior
probability of being a member of segment 2 to be a function of demographic and shopping
characteristics, as shown below (Gupta and Chintagunta 1994).
Z is a row-vector of demographic and shopping characteristics of household h, and
the corresponding column-vector of parameters. We include the following variables in
family size, income (dollars), employment status (1 if female head of household works more than
35 hours per week, and 0 otherwise), education (1 if female head attended college or above, and
0 otherwise), average quantity (rolls per purchase occasion), consumption rate (rolls per week),
shopping frequency (total number of shopping trips), and purchase frequency (total number of
purchase occasions). The results of this analysis are given in Table 6. They show that family size,
average quantity, consumption rate and purchase frequency all have positive effects on the
household’s probability of belonging to segment 2. Taken together with our earlier findings that
price deals have stronger direct and indirect impact on segment 2, this suggests that larger
families and heavy users are more responsive to deals, consistent with the findings in Erdem,
Mayhew and Sun (2000), Krishna, Currim and Shoemaker (1991), and Vanhuele and Dreze
(2002). We also find that employment status and education level of female head of household,
and shopping frequency all have negative effects on the household’s probability of belonging to
segment 2. The results suggest that households who shop less frequently may be more likely to
utilize the limited information used to learn about future prices and then account for such
learning in their purchasing decisions, consistent with findings in Yadav and Seiders (1998). The
results also indicate that the indirect impact of current price deals is smaller for more educated
and employed consumers, who have higher costs of time, and will, therefore, may engage in less
[Insert Table 6 Here]
Brand-Loyals versus Brand-Switchers
Next, we are interested in understanding whether brand-loyals and brand-switchers differ
in how price deals affect their learning on future deals, as well as whether the impact is different
for the two groups.10 For example, brand-loyals, who have high psychological cost of not having
their favorite brand, are likely to focus on forming expectation about deal timing to strategically
manage their inventories. On the other hand, brand-switchers, who are inclined to switch among
brands, may be more focused on whether the current opportunity is right to purchase the focal
brand and therefore, are more likely to undertake the deal probability learning. In order to gain
this understanding, we first classify all the available households into two loyalty groups, a priori,
as in Krishnamurthi, Mazumdar and Raj (1992). Specifically, we classify a household as a brand-
loyal if the household bought a single brand on more than 50 percent of its purchase occasions,
and as a brand-switcher otherwise. This yields 68 brand-loyals and 44 brand-switchers. We then
estimate both versions of our proposed model – PROPOS-P and PROPOS-T – separately for the
two groups of households.
The goodness of the fit measures show that for both brand-loyals and brand-switchers,
the deal-probability learning process better describes formation of deal expectations than does
the deal-timing learning process, contrary to our prior expectation. This implies that when
observing a deal price for a brand in paper towels, both brand-loyals and brand-switchers expect
the deal price to persist in to the immediate future, and the price deal lowers the attractiveness of
the current deal.
We report the results of the incidence sub-model of PROPOS-P, separately for brand-
loyals and brand-switchers, in Table 7. Both direct and indirect impacts of current prices are
larger for brand-loyals than for brand-switchers (2.70 and -2.16 for brand-loyals, and 1.70 and -
0.81 for brand-switchers), with the differences in magnitude being greater for the indirect impact.
This corroborates the findings in Rajendran and Tellis (1994) and Mazumdar and Papatla (2000)
10 Involvement theory can be used to motivate how different degrees of involvement among consumers would
differently influence how they form price expectations (see, for example, Chandrashekaran and Grewal 2003).
that brand-loyals show more temporal reference price effects than brand-switchers. The findings
are also consistent with those in Chan, Narasimhan and Zhang (2008) that brand-loyals show
greater immediate and long-term responses to current price reductions than brand-switchers do.
The memory decay parameter is 1 for brand-loyals, and close to 0 for brand-switchers. This
implies that when learning about future deals, brand-loyals track the entire history of price deals
on their preferred brands, while brand-switchers primarily rely on current deals only. This is
consistent with the findings in Krishna, Currim and Shoemaker (1991) and Krishna (1991) that
brand-loyals have more accurate perceptions of deal frequencies than brand-switchers, and the
findings in Vanhuele and Dreze (2002) that brand-loyals have better price knowledge than
[Insert Table 7 Here]
We report the results of the brand choice sub-model of PROPOS-P in Table 8. As
expected, the coefficient of price is much higher for brand-switchers (-9.57) than for brand-
loyals (-3.25), suggesting that brand-switchers are more price-sensitive in brand choice decisions.
In the quantity model, while current prices are found to have a direct impact on both brand-loyals
and brand-switchers, they have no indirect impact on either group. Furthermore, there are no
discernible differences in parameter estimates between brand-loyals and brand-switchers.11
[Insert Table 8 Here]
Heterogeneity in Learning
Consumers may be heterogeneous in the processes of learning about future deals. In other
words, when observing a deal price on a brand, some consumers may expect the deal price to
11 The estimation results of the quantity model are available from the authors.
persist in to the immediate future while other consumers may expect the deal price to be retracted
in the immediate future and reappear some periods later. To understand the heterogeneity in
consumer learning, we estimate a finite mixture model where we assume that there are two
segments of households that are different in their learning processes. It turns out that 74 percent
of households in our dataset engage in deal-probability learning, while 26 percent use deal-
timing learning. The estimated parameters of the incidence model show that the current prices
have stronger direct effects (2.33 vs. 1.88) but weaker indirect effects (-1.07 vs. -1.47) on the
deal-probability learning households than on the deal-timing learning households. The deal-
probability learning households also show stronger preferences to higher-priced brands like
Bounty, Viva and Scott, while being more price-sensitive (-6.72 vs. -4.15). Moreover, household
inventory and consumption have less impact on the quantity decisions of deal-timing learning
Sales Prediction in Holdout Period
Next, we run a policy simulation to demonstrate the profit implications of incorporating
the indirect impact of price deals through the formation of consumers’ future price expectations.
We generate the expected sales for each brand during the holdout period as predicted by the
proposed model with deal-probability learning, and then compare this to the expected sales
implied by the benchmark model that ignores the indirect effects of price deals.
The expected sales from household h for brand j in week t,
, can be calculated as
hjt ht hjt
E Qyy j qqq
12 The estimation results for the finite mixture model are available from authors.
yy j qq
is the probability that household h purchases q units of brand j
at week t. The total expected sales in T period from all households,
, then can be
jhs ht hjt
E Qfyy j qqq
Under the proposed model and the benchmark model, we respectively simulate the total
expected sales for each brand by aggregating the predicted choices over all households. For this
purpose, we use the estimated parameters from the calibration sample, and assume prices,
features and displays of brands, and household inventories to take the observed values in the
holdout sample. The results are reported in Table 9. Table 9 shows that except for the generic
brand, the benchmark model - which does not incorporate the indirect effects of price deals or
consumer learning - significantly overstates the predicted sales of brands, and is overly
optimistic about the sales effects of price deals. For example, the benchmark model predicts that
the total sales for the Scott brand will be 1709 rolls while our proposed model predicts that only
646 rolls will be sold, the overstatement being as high as 164%.
[Insert Table 9 Here]
We build an econometric model that allows brands’ price deals to affect consumers’
purchasing decisions not only directly – through their effect on consumer utilities today – but
also indirectly – through their effects on the formation of consumers’ future price expectations.
We examine two alternative learning processes of future deals to explain how the price deals
affect consumers’ purchase decisions indirectly: (1) deal-probability learning, which assumes
that consumers update their beliefs about the likelihood of deal occurrence on a brand according
to a modified Beta-Bernoulli process, and (2) deal-timing learning, which assumes that
consumers update their beliefs about a brand’s inter-deal times according to a Gamma-Poisson
process. These two learning processes have opposite implications on consumers’ current
purchase behavior. For example, upon seeing a deal on a brand in the current period, under deal-
probability learning, a consumer will expect the future price to continue to be low, resulting in
lower attractiveness of the current deal to the consumer and, therefore incidence deceleration. On
the other hand, under deal-timing learning, a consumer will expect the future price to be higher,
resulting in greater attractiveness of the current deal to the consumer and, therefore, incidence
acceleration. We embed consumers’ expected future prices – constructed using one of these two
learning processes – within a joint model of consumer purchase decisions – incidence, brand
choice and quantity – while explicitly correcting for the effects of endogenous self-selectivity in
the discrete quantity outcomes.
Using scanner panel data on paper towel purchases, we find that the indirect effects of
price deals are important in explaining observed incidence outcomes in the category. We find
that the deal-probability learning process better describes consumers’ learning on future deals
than does the deal-timing learning process for our data. The indirect impact of price deals is
found to be greater for (1) brand-loyals than for brand-switchers, and (2) infrequent shoppers
than for frequent shoppers. We also run a policy simulation to demonstrate the overstatement of
sales prediction with price deals when the indirect effects of price deals are ignored.
The key managerial take-away from our analyses is that price deals have not only a direct
impact, but also an indirect impact – through their influence on consumers’ expectations of
future prices – on demand for the promoted brand. Our finding that the deal-probability learning
process better describes consumers’ learning on future deals than the deal-timing learning
process implies that consumers would accelerate their purchases less when they see a price deal
than what is implied by a model that ignores the indirect impact of current deals. This is because
the deal-probability learning process implies that when consumers see a deal, while such a deal
increases the attractiveness of the promoted brand thus leading to incidence acceleration, the deal
also leads consumers to believe that it will persist in the immediate future, thus leading to
incidence deceleration. To the extent that price deals are sometimes used by retailers to clear
excess inventory (Blattberg, Eppen and Lieberman 1981), our findings imply that a deal may not
be as effective in achieving this purpose since the indirect effect of the deal partly decelerates
consumer purchases. On the other hand, if the purpose of a deal is to increase retail sales for the
promoted brand over an extended period of time, especially during periods when prices have
reverted to their original (high) levels, our findings should be encouraging to retailers because
some consumers who delay purchasing during a deal, expecting the deal to persist, may end up
buying the product in the future at higher prices due to inventory pressure.
Our finding that the direct and indirect impacts of prices are higher for brand-loyals than
brand-switchers suggests the following cautionary note for manufacturers: When manufacturers
induce retailers to offer price deals on their brands to attract incremental demand from brand-
switchers, who would not have bought the brand at regular prices, manufacturers must explicitly
account for the decreased profits from the brand-loyals (who, in fact, are responding more to
deals than the brand-switchers!). More generally, correctly accounting for the impact of
consumers’ deal knowledge and responsiveness on seller profits is an issue of significant
managerial interest (McAlister, George and Chien 2009, Petersen et al. 2009).
There are some possible areas of future research. First, it will be useful to compare the
two learning processes on a wide variety of product categories. This will help examine whether
the preference of one learning model to the other is linked to characteristics of individual
categories, e.g., the deal patterns, the purchase frequencies, etc. Second, we assume that deal
events are independent across brands. This may not be the case if the retailer is strategically
deciding which brand to promote on a given week and consumers are aware of the strategic
choices. Explicitly investigating the effects of the correlations between brands’ periodic deals on
consumers’ deal learning models will be useful. Third, one can examine how the indirect impact
of price deals will be moderated if time-varying brand loyalty and category purchase volumes are
incorporated in the learning processes (Estelami and Lehmann 2001). Last, it will be interesting
to investigate the effects of future expectations of displays and features on consumer purchase
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Figure 1. Time Series Plot of the Prices of Viva Paper Towels
Table 1. Descriptive Statistics over Study Period
Brand Avg. Purchase
Table 2. Comparison of Model Fits
PROPOS-P PROPOS-T BENCH-NF BENCH-NC
Number of Parameters 49 47 43 41
Calibration Sample LL -6394.77 -6407.45 -6413.88 -6446.41
AIC 12887.54 12908.90 12913.76 12974.82
BIC 13020.75 13036.67 13030.66 13086.28
Holdout Sample LL -2417.16 -2437.09 -2427.38 -2443.07
Table 3. Estimated Parameters of the Incidence Model
PROPOS-P Segment 1 PROPOS-P Segment 2
Note: Standard errors are in parentheses.
Table 4. Estimated Parameters of the Brand Choice Model
PROPOS-P Segment 1
PROPOS-P Segment 2
Note: Standard errors are in parentheses.
Table 5. Estimated Parameters of the Quantity Model
PROPOS-P Segment 1
PROPOS-P Segment 2
Note: Standard errors are in parentheses.
Table 6. Hierarchical Regression of Segment Membership Probabilities versus Household
Note: Standard errors are in parentheses.
PROPOS - P
Table 7. Estimation of the Incidence Model of Brand-Loyals versus Brand-Switchers
Note: Standard errors are in parentheses.
Table 8. Estimation of the Brand Choice Model for Brand-Loyals versus Brand-Switchers
Note: Standard errors are in parentheses.
Table 9. Total Expected Sales for Each Brand during the Holdout Period
Proposed Model (in rolls) Benchmark Model (in rolls) Overstatement by Benchmark Model
Private Label 118 143 20.8%
Generic 80 59 -26.3%
Bounty 819 2038 148.8%
Viva 273 687 151.2%
Sparkle 26 53 102.9%
Scott 646 1709 164.4%
Gala 18 36 104.3%
Mardi Gras 27 56 108.2%
APPENDIX A. Details on the Estimation of a Joint Model of Incidence, Brand Choice and
Our objective is to estimate the parameters of the joint model of incidence, brand choice
and quantity, as well as to test the indirect effects of price deals on incidence and quantity. To
this effect, we estimate the parameters
at the household-level, where
the 4 parameters in the incidence model,
contains the (J−1)+3 parameters in the brand choice
contains the 5 parameters in the quantity model. Assuming a discrete random
effects specification for heterogeneity (as in Kamakura and Russell 1989) would yield a total of
S * ((J − 1) + 12) + S – 1 estimable parameters.
The probability of an observed purchase at the household-level can be written as follows.
which implies that the household-level likelihood function can then be written as
s h s
L f L
h sht ht
sf is the mass of support point s.
One technical concern that arises in the estimation is the fact that a household’s quantity
decision may be correlated, for unobserved reasons, with its incidence and brand choice
decisions. Therefore, we adopt a technique for selectivity bias correction in discrete outcomes
(Zhang, Seetharaman and Narasimhan 2005), and we describe this technique in our context next.
Under the assumption of unobserved correlations between a household’s three purchase
decisions, the likelihood of an observed purchase can be written as follows.
yyj qqyyj qq
which can be rewritten as
,, Pr( 1 ;
htht hjt hjt
stands for the cdf of a trivariate normal distribution with covariance matrix ,
stands for the cdf of a standard normal distribution.
We ignore unobserved correlations between a household’s incidence and brand choice
decisions in the proposed model because the inclusive value measure already captures
dependencies between the two decisions, in the spirit of the nested logit model. However, we do
estimate the unobserved correlation between incidence and quantity, as well as the unobserved
correlations between the chosen brand and the corresponding quantity.
The proposed likelihood function is maximized using gradient-based routines in
SAS/IML. The optimal number of support points for the unobserved heterogeneity distribution,
i.e., S, is identified by sequentially adding supports and re-estimating the model, until there is no
further improvement in the Bayesian Information Criterion (BIC) of model fit.
APPENDIX B. The Derivation of Expected Future Brand Utility
denote the deterministic component of the expected (indirect) utility of
household h for brand j at shopping occasion t + m. Then,
hj tm hjh hj tmh hj tmhhj tm
EVEP ED EF
hj tm hj tmhj tm
stand for the expected price, display and feature respectively for
brand j at a future time t + m for household h. Since in this study we focus on the impact of
households’ future price expectations, we make a simplification that
hj tm hjt
. This yields
hj tm hjhhj tmhjd hj tmhjrh hjthhjt
hj tm hjd hj tmhjr
hjd hjh hjdh hjdh hjd
hjrhjh hjrh hjrhhjr
P are the deal price and regular price associated with brand j, respectively.
41 Download full-text
We then construct a term, the expected future brand utility,
, which is the future
counterpart of the deterministic component of the (indirect) utility of household h for brand j at
shopping trip t,
incorporates household h’s expectations of the brand utility for the
future periods after trip t.
Under deal-probability learning,
hjt hj tmhj tm hjdhj tmhjr
, for all 0.
Under deal-timing learning, since the household forms expectations on when the next
deal will occur (among all periods starting from t + 1), we first obtain the present value
(at t+1) of the future brand utilities over time, PV, as shown below.
where γ is a time discount factor, which lies between 0 and 1. Then, we let
to the equivalent average future brand utility, which is the product of PV and (1 − ) as follows.
is a Poisson hazard function given in