Modeling Marketing Dynamics by Time Series Econometrics

Time-series econometrics has made several important contributions in
fundamental areas of marketing. As reviewed in Dekimpe and Hanssens (2000,
Table 1), time-series (TS) techniques were initially used in marketing (1)
for forecasting purposes, (2) to determine the temporal ordering among
variables through Granger-causality tests, or (3) to determine the over-
time impact of marketing variables (e.g. through transfer-function
analysis). Recently, there has been a renewed interest in the use of TS-
techniques, not only to demonstrate the existence of certain substantive
marketing phenomena, but also to derive empirical generalizations on their
relative size and frequency of occurrence.[1] Studies in the former
tradition have, for example, shown that time-series techniques can be used
to quantify short-term, long-term and permanent effects (Dekimpe and
Hanssens 1995), momentum (Bronnenberg, Mahajan and Vanhonacker 2000),
business-as-usual, hysteresis and escalation (Dekimpe and Hanssens 1999),
ad copy and repetition wearout (Naik, Mantrala, Sawyer 1998), half-life of
ads (Naik 1999), synergy (Naik and Raman 2003), and strategic foresight
(Naik, Raman and Winer 2005). Studies in the latter tradition include Nijs
et al. (2001), Pauwels and Srinivasan (2004), and Srinivasan et al. (2004).
A typical design in these studies is a two-stage approach, where, the same
time-series technique is first applied to a multitude of brands and/or
product categories, after which one tries to explain the observed
variability in various summary statistics (e.g. short or long-run
elasticity estimates) through a number of marketing-theory based
hypotheses. To this end, a more marketing-theory grounded approach to TS
modeling was adopted. Moreover, other key challenges identified in Dekimpe
and Hanssens (2000), such as the lack of longitudinal data and the lack of
dedicated time-series software, have been overcome in recent years.
Still, important research opportunities and challenges remain, which
were summarized in a number of challenges in the presentation by Dekimpe
and Hanssens, and elaborated upon by various other presentations as well as
round-table discussions, at the conference 'Modeling Marketing Dynamics by
Time Series Econometrics', held at the Tuck School of Business at Dartmouth
in September 2004. These challenges (summarized in Table 1) are the focus
of this paper.[2] 1. Challenge 1: Dealing with recent data richness
Dekimpe and Hanssens (2000) identified the shortage of good time-series
data as one of the main obstacles to the initial diffusion of time-series
methods into the marketing literature. However, they acknowledged that
recent developments, such as the growing availability of longer series of
scanner data, considerably alleviated this concern (see e.g., Dekimpe,
Hanssens and Silva-Risso 1999; Pauwels et al. 2002; Pauwels and Srinivasan
2004, and Nijs et al. 2001 for recent applications of TS-techniques to
scanner-based data).[3]
However, data have not only become available over longer time spans, they
also became available at ever more disaggregate levels. This enabled
researchers to build intricate dynamic models at the individual-store level
(e.g., Srinivasan et al. 2003), the consumer-segment level (Lim, Currim and
Andrews 2004), or even at the individual SKU-level (e.g., Macé and Neslin
2004, Pauwels, Naik and Mela 2004). Moreover, data now become available
at ever smaller time intervals. Still, this recent data explosion has also
resulted in a set of new concerns, such as (i) the issue of data
aggregation in time-series models, (ii) potential over-parameterization
when adopting a systems approach, and (iii) the common (yet not consistent)
practice of data pruning. 1. 1 Data aggregation
Cross-sectional heterogeneity and aggregation bias have been important
subjects in both economics (Pesaran and Smith 1995) and marketing (e.g.,
Allenby and Rossi 1991, Christen et al. 1997). Recent marketing time-
series (TS) studies have taken a variety of approaches to deal with this
issue. While most studies (perhaps at the explicit request of reviewers),
acknowledge the potential bias that emerges when using arithmetically
averaged data in the estimation of non-linear models, few recognize that
the neglect of (slope) heterogeneity across the entities over which the
data are averaged is even more serious in dynamic models (a notable
exception is Horváth and Wieringa 2004). Indeed, in models with serially-
correlated lagged endogenous variables, incorrectly ignoring coefficient
heterogeneity induces serial correlation in the error term, which in turn
results in inconsistent parameter estimates (see Pesaran and Smith 1995 for
an in-depth discussion). This applies to both linear and nonlinear models.
As such, the approach used in Nijs et al. (2001) and Srinivasan et al.
(2004) to compare the IRFs of linear and multiplicative models may not be
fully informative on the presence/absence of aggregation bias in dynamic
models. Horváth and Wieringa (2003) advocate the use of preliminary
pooling tests to determine the appropriate level of parameter heterogeneity
that should be allowed for. In their empirical application (see also
Horváth, Leeflang, Wieringa and Wittink 2004), a fixed-effects VAR model is
used where different intercepts but common slopes are estimated across more
than 20 stores. More research is needed, however, on how to proceed when
the preliminary tests indicate that the slopes cannot be treated as
homogenous (we elaborate on this issue below).
To further complicate matters, aggregation can take place across multiple
dimensions: across the stores in a country (Nijs et al. 2001), across the
stores in a chain (Srinivasan et al. 2004) or across the SKUs of a brand
(Pauwels et al. 2004a). Thus far, studies that focus on the potential bias
arising from aggregating across one dimension, have tended to ignore that
the same problem may also arise because of the aggregation across the other
dimensions. For example, even if one would estimate response models at the
SKU level in individual stores, there might still be the issue whether all
consumer segments have the same short- and/or long-run response parameters.
Such heterogeneity was demonstrated at the Tuck conference by Imran
Currim, who obtained different response patterns to price promotions for
heavy versus light users in a category level analysis, and for loyal versus
switching segments in a brand level analysis. First, light users are found
to have longer adjustment periods and larger adjustment effects but smaller
total effects for perishable products. For non-perishable products, heavy
users are found to exhibit a post-promotion dip, which reduces the total
effect of the promotion relative to light users. Moreover, consumers loyal
to other brands have longer adjustment periods, and larger adjustment and
total effects than either consumers loyal to the focal brand or switchers.
Finally, segment-level VARX models were found to improve forecasts over
their aggregate counterparts for two of four product categories studied.
When segment-level VARX models do not offer better forecasts than their
aggregate counterparts, the segment-level RMSE is usually close to its
aggregate-level counterpart, so that not much is lost in using segment-
level VARX models (Lim, Currim, and Andrews 2004). Discussion revealed that
future research could investigate whether price promotions can pull
consumers from one segment to the other. In addition, while a priori
segmentation (e.g., heavy vs. light users, loyals vs. switchers) results in
insights which are useful for marketing managers, it may not be the most
statistically efficient way to segment consumers, because it does not
necessarily maximize (minimize) differences across (within) segments.
Consequently, it may be useful to develop a household-level approach based
on a posteriori segmentation. Obviously, more research is needed on how to
best accommodate these various sources of cross-sectional heterogeneity in
time-series models.
Thus far, we focused on cross-sectional aggregation across stores, SKUs
or customers. However, data have not only become available on smaller
entities, but also at ever smaller time intervals. This opens up a whole
new set of research opportunities. Two of them were specifically
considered at the Tuck conference: Tellis and Franses (2004) reconsidered
the optimal data interval issue for econometric models of advertising
carryover, while Ghysels (2004) explored the econometric consequences of
mixed data sampling models, i.e., where different variables have a
different data-collection frequency. Indeed, most time-series and marketing
models to date assume a common frequency of data collection across all
variables in the model. However, nowadays, data on market performance and
marketing actions may come in different frequencies (e.g., weekly for price
and sales, monthly for advertising, quarterly for firm earnings). Ghysels,
Santa-Clara and Valkanov (2003a) developed Mixed Data Sampling (MIDAS)
Regression methods to deal with this issue. This approach constructs
regressions combining data with different sampling frequencies. In essence,
MIDAS constructs a polynomial of coefficients on lagged independent
variables, governed by a small set of hyperparameters. Numerous
applications are already available in the finance area (see e.g., Forsberg
and Ghysels (2004), Ghysels, Santa-Clara and Valkanov 2003 b, c). However,
in current MIDAS applications, the right-hand side variable is the most-
frequently sampled variable. In a marketing setting, this may involve
linking weekly marketing actions to quarterly firm performance, or using
very fine-tuned Internet marketing actions to explain slower changing (and
less frequently sampled) consumer attitudes. However, other marketing
settings face the opposite problem, as independent variables such as
ad