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Using cointegration analysis for modeling marketing interactions in
dynamic environments: methodological issues and an empirical illustration
Rajdeep Grewala,*, Jeffrey A. Millsb, Raj Mehtab, Sudesh Mujumdarb
aDepartment of Marketing, Washington State University, Pullman, WA, 99164-4730 USAb
University of Cincinnati, Cincinnati, OH, USA
Received 6 June 1999; accepted 2 February 2000
Abstract
The authors argue that cointegration analysis is an intriguing development for analyzing marketing interactions in dynamic environments.
Methodologically, the use of cointegration analysis requires statistical tests to determine whether this technique is appropriate for the system
under investigation and, if it is appropriate, other statistical tests are needed to interpret the results. The authors collate a set of statistical tests
and techniques to advance a comprehensive methodological framework that utilizes cointegration analysis to examine marketing interactions
in dynamic environments. The framework is useful for analyzing marketing parameter functions with time-varying coefficients to investigate
the relationship between market performance (e.g., sales, market share), marketing effort (e.g., advertising, sales promotion), and
environmental conditions (e.g., market growth, inflation). The authors illustrate the utility of the framework for the famous case of Lydia
Pinkham Medicine Company (LPMC). D 2000 Elsevier Science Inc. All rights reserved.
Keywords: Cointegration analysis; Marketing interactions; Dynamic environments; Lydia Pinkham Medicine Company
1. Introduction
At the nucleus of marketing research and theorizing, lie
marketing interactions. Marketing interaction mechanisms
determine the relationship between marketing performance
(e.g., sales, market share), marketing effort (e.g., advertis-
ing, personal selling), and environmental conditions (e.g.,
growth rate, competitive activities). Typically, researchers
use market response models to investigate marketing inter-
actions in order to examine the behavior of markets and
predict the impact of marketing actions (Hanssens et al.,
1990; Leone, 1995). Given the importance of marketinginteractions, scholars have proposed various methodological
frameworks to model these interactions (cf., Wildt and
Winer, 1983; Gatignon and Hanssens, 1987). Recent meth-
odological advances in econometrics concerning cointegra-
tion analysis provide a new technique to analyze these
interactions. In this paper, we utilize recent advances in
econometrics concerning cointegration analysis to illustrate
a framework for analyzing marketing interactions.
Since the path breaking paper by Granger (1981) and the
subsequent conceptual and methodological developments
by Engle and Granger (1987), cointegration analysis has
become an integral part of non-stationary time series ana-
lysis. Murray (1994) provided an intuitive explanation of
cointegration. Murray (1994) uses the analogy of a drunkard
walking her dog to explain the notion of cointegration. The
drunk and her dog wander aimlessly, but make sure that they
have an eye on each other and do not separate by more than
a certain distance. Thus, even though both of them do not
know where they are going, they do know that they are
going together. In a way, the drunk and her dog arecointegrated. Formally speaking, two or more non-station-
ary variables, which are integrated of the same order, are
cointegrated if there exists a linear combination of these
variables that is stationary. Specifically, cointegration ana-
lysis involves time series data and multi-equation time series
models, allowing for systematic and random parameter
variation, with two or more variables.
Marketing researchers have used multi-equation time
series models to investigate various phenomena. For exam-
ple, such models have been used to study the interaction
between the structure of marketing function (brand vs.
category management) and competition (cf., Zenor, 1994;
* Corresponding author. Tel.: +1-509-335-5848; fax: +1-509-335-
3865.
E-mail address: [email protected] (R. Grewal).
0148-2963/01/$ see front matterD 2000 Elsevier Science Inc. All rights reserved.
PII: S 0 1 4 8 - 2 9 6 3 ( 9 9 ) 0 0 0 5 4 - 5
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Curry et al., 1995); advertising and price sensitivity (cf.,
Eskin and Baron, 1977; Krishnamurthi and Raj, 1985);
advertising, temperature, price, and consumer expenditure
(Franses, 1991); advertising, price sensitivity, and competi-
tive reaction (Gatignon, 1984); advertising and product
quality (Kuehn, 1962); advertising and product availability
(Kuehn, 1962; Parsons, 1974); advertising competition(Erickson, 1995); advertising expenditure and advertising
medium (Prasad and Ring, 1976); advertising and prior
sales person contact (Swinyard and Ray, 1977); advertising
and personal selling (Carroll et al., 1985); competitive
behavior (Hanssens, 1980b); sales force effectiveness and
environmental hostility (Gatignon and Hanssens, 1987);
integrated marketing communications (cf., Beard 1996;
Hutton, 1996); persistence modeling (Dekimpe and Hans-
sens, 1995a,b); and consumer confidence (Kumar et al.,
1995) among others.
In most cases, conventional multi-equation time series
analysis involves the use of Vector Autoregressive (VAR)models with two or more stationary variables (cf. Hamil-
ton, 1994; Enders, 1995). Typically, one differences non-
stationary difference variables to make them stationary
and then uses them in a VAR model to investigate
underlying data generation mechanisms (cf., Curry et al.,
1995; Dekimpe and Hanssens, 1995b). Differencing non-
stationary variables results in loss of information (cf.,
Enders, 1995). Cointegration analysis provides a metho-
dology for analyzing non-stationary variables, without
making them stationary, thereby preventing loss of infor-
mation due to differencing.
Examples of marketing systems with non-stationary
variables, which are related to each other and, thus, would
benefit from cointegration analysis are plentiful. For in-
stance, in a typical diffusion of innovation setting, where a
new product is replacing an existing product, the sales of
these two products, promotion and advertising spending,
along with sales of competing products, are likely to move
together and thereby be cointegrated. In addition, cointegra-
tion analysis is a useful tool to examine sales force effec-
tiveness (cf., Gatignon and Hanssens, 1987) and in
understanding the implications of various pricing decisions
and strategies on marketing performance (cf., Curry, 1993).
These explications for application of cointegration analysis
in marketing are by no means exhaustive and are meant asmere illustrations of the usefulness of cointegration analysis
in investigating marketing interactions.
Marketing researchers are just beginning to use coin-
tegration analysis to study marketing interactions. Specifi-
cally, a couple of studies (Baghestani, 1991; Zanias, 1994)
examine the advertising sales relationship and Franses
(1994) has studied the sales of new products. These studies
and our illustrations demonstrate the utility of cointegration
analysis; however, the intricate nature of theoretical re-
search on cointegration limits its use. Our primary objec-
tive is to summarize theoretical cointegration literature to
facilitate its use by marketing scholars. Utilizing cointegra-
tion analysis requires that all data series under investigation
to be integrated of the same order, which implies that one
has to perform statistical tests on the data series under
investigation to make sure that the system under investiga-
tion is suitable for cointegration analysis. In addition,
drawing conclusions from the estimation results of coin-
tegration analysis requires more statistical tests. The mainobjective of this article is to demonstrate a comprehensive
methodological framework for analyzing multi-equation
time series data using cointegration analysis. Such a frame-
work is of considerable interest to both marketing scientists
and marketing managers, as better understanding of mar-
keting interactions is of interest to both parties. Both are
interested in marketing interactions because they want to
know what drives marketing performance. Our framework
provides both parties with tools and a systematic method to
study these interactions. Further, a comprehensive and
consistent framework makes it easy to identify unifying
principles that aid in empirical generalization and advance-ment of marketing science (cf., Bass, 1993, 1995; Bass and
Wind, 1995). Finally, such a framework would be useful
for pedagogic exposition.
To achieve our objectives, we survey recent develop-
ments in the econometrics and time series literature to
collate a set of statistical tests and estimation techniques,
which are useful in exploration of marketing interactions.1
Based on our literature review, we illustrate the usefulness
of cointegration analysis in marketing and provide the
rationale for expecting specific type of behavior from
various marketing variables. Furthermore, we demonstrate
the proposed framework to model marketing interactions
for the famous case of Lydia Pinkham Medicine Com-
pany (LPMC).
2. Methodological framework and conceptual
underpinnings
Marketing interactions, by their very definition, imply
that interactions among several marketing effort variables,
along with their interaction with environmental variables,
determine marketing performance. Further, when firms take
decisions concerning marketing effort, they may take mar-
keting performance into consideration. In addition, environ-ment interacts with both performance and effort to further
complicate matters. For example, the time of the year and
advertising expenditure in the previous month together
determine sales which in turn determines advertising ex-
penditure this month which in turn influences sales. Multi-
equation modeling helps in capturing this dynamic behavior
1 We choose the statistical tests that in our opinion are most
appropriate. We do not claim that these are the only or universally the
best statistical tests for the purpose. Our objective is to provide and
illustrate the steps of our framework and not to determine the goodness of
one test vis-a-vis another.
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in the market place. In Appendix A, we present a typical
multi-equation model, which captures the dynamics of
marketing interactions.
To capture marketing interactions in a cointegration
framework, we propose a nine-step framework to investi-
gate the complex system represented in the two equations
we present in Appendix A (Fig. 1). In the first four steps ofthe framework, i.e., unit root test, structural break test, unit
roots with structural tests, and reconciling the results from
the two unit root tests, we are concerned with determining
the data generation process of each individual variables.
Uncovering these aspects of the data generating mechan-
isms, provides information whether the variables being
studied are suitable for cointegration analysis or not. Sub-
sequently, in the next two tests, i.e., cointegration test and
estimation techniques, we use the results from the first four
steps to model the interactions between environment, effort,
and performance variables. Finally, in the final three steps,i.e., Granger causality, variance decomposition, and impulse
response functions (IRFs), we use the inputs from the
cointegration results to uncover interrelationships between
the variables under investigation. In the remainder of this
Fig. 1. Methodological framework.
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section, we enumerate on each of the nine steps in our
framework and provide reasons for expecting certain beha-
vior by marketing performance variables, marketing effort
variables, and environmental variables.
2.1. Unit roots2
Dekimpe and Hanssens (1995a) operationalized the
concept of stationary and evolving markets based on the
unit root tests. The unit root tests examine each time series
to determine whether the mean, variance, or autocorrela-
tion of the underlying data generation process for each of
these variables increases or decreases over time. A time
series whose mean or variance or autocorrelation either
vary over time or are not finite might be non-stationary
and may have a unit root. Classical linear regression
models requires data series under investigation to be
stationary and if this assumption is violated it leads to
the problem of spurious regression (Granger and Newbold,1974). Further, cointegration analysis requires all series
under investigation to be non-stationary. Hence, it is
important to identify, initially, the order of integration of
the data generation process.
One could hypothesize many marketing variables to be
non-stationary based on their data generation process (De-
kimpe and Hanssens, 1995b). For example, the vast litera-
ture on diffusion of innovation suggests that the sales
figures for a successful new product will grow during its
initial years (cf., Mahajan et al., 1990). Further, one can
expect price of some products to increase over time, perhaps
due to inflation, and thereby be non-stationary. In addition,
it is possible that price of some products decreases over time
due to experience curve effects (Bass, 1995), thereby
representing a non-stationary data generation process.
2.2. Structural breaks
The structural breaks represent a point or an interval in
time, which denote modifications in the underlying data
generation process. The modifying agent is usually an
extraneous event. For example, structural breaks in sales
might be due to interventions of federal regulatory agencies,
as in the case of tobacco industry, where federal regulations
on how and where to sell tobacco products are plentiful (cf.,Rogers, 1994; Economist, 1996; France, 1996). Other ex-
amples of structural breaks include competitive new product
introductions and new generation of products (cf., Norton
and Bass, 1987, 1992; Mahajan et al., 1993).
While analyzing 14 macroeconomic time series, Perron
(1989) provided a startling finding that after correcting for
structural breaks, like the exogenous oil price shock of
1973, most of the macroeconomic series are either sta-
tionary or trend-stationary. If a series is stationary or trend-
stationary, cointegration analysis is not an option. Clearly,
it is important to account for structural breaks when
modeling economic time series to identify modifications
in the data generation process. As Perron (1989) demon-strated, overlooking structural breaks might mislead con-
clusions concerning the underlying data generation
process, which may lead to model misspecification and
wrong conclusions.
There are two major issues concerning structural breaks.
The first concerns the time when the break has its effect on
the underlying data generation process: immediately after
the event of interest or after a certain lag. Typically, either
of the two cases is possible. If the event of interest is high-
profile (e.g., oil shock of 1973), we might expect an
immediate change. For low-profile interventions, like the
actions of competitors or reprimand by federal agencies, thestructural change might be delayed, as the information
needs time to diffuse through the social system (Mahajan
et al., 1990).
The second issue concerns the nature of the break. One
can expect the mean of a series to change, or the slope of
the data series to change, or changes in both mean and
slope. An example of change in mean would be high-
profile shocks, though this effect might be temporary.
Interventions due to sales promotions or federal legisla-
tion's fall in this domain. Changes in slope might be a
result of federal regulations, competitive interventions, etc.,
which need time to implement and diffuse through the
social system. For instance, let us say that a federal agency
issues a cease and desist order. The effect of this order
could be gradual as information diffuses through the
concerned social system (Mahajan et al., 1990). Finally, a
successful new product introduction by the competitor can
instantaneously reduce a firm's sales (change in mean) and,
in addition, after the instantaneous effect, the influence of
the new product may gradually erode more sales (change
in slope).
The time of structural change and the nature of the
change are interesting in and of themselves. In addition,
these univariate tests shed light on modifications in the data
generation process for the time period under investigation.
2.3. Unit roots after incorporating structural breaks
Perron (1989) found most macroeconomic data series to
be either stationary or trend-stationary after incorporating
structural breaks. Traditional unit root tests (cf., Dickey
and Fuller, 1981; Phillips and Perron, 1988) do not
compensate for structural changes. Thus, it is possible
that these traditional tests find unit roots in stationary
process due to structural breaks. Hence, it becomes
important to account for unit roots after incorporating
structural breaks.
2 In the remainder of Section 3, we elaborate on the rationale for
expecting specific behavior form marketing variables. The statistical
aspects of these tests and estimation techniques are discussed in Section
4, where we illustrate the framework for the famous case of Lydia
Pinkham Medicine.
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2.4. Reconciling unit root tests before and after
incorporating structural breaks
The main reason to perform unit root tests after incor-
porating structural breaks is to overrule the possibility that a
structural break may be causing misperceptions concerning
the stationarity of the variables under study. Further, thereexists a possibility that the unit root tests before and after
incorporating structural breaks may not agree. If the results
agree then we establish robustness of the findings. If the
results do not agree, Perron (1989) suggests that one should
proceed with and estimate models with the results from both
unit root tests.
So far, we have laid down the steps to investigate the
underlying data generation process of each individual data
series and have not examined the interaction between these
data series. One can use the results from these steps to
formulate an appropriate model for further investigation.
Further, if we have two or more non-stationary time series,there is a possibility that these variables may be cointe-
grated. In such a case, we must proceed with the coin-
tegration tests, otherwise a VAR with stationary variables
is appropriate.
2.5. Cointegration
In this step, we decide whether cointegration analysis is
appropriate or not. If the variables under investigation are
non-stationary and integrated of the same order, cointegra-
tion analysis is mandatory. It is important to identify a
cointegrating relationship between non-stationary variables
because such a relationship implies an equilibrium between
these variables and overlooking this equilibrium results in
misspecifications in the error term (cf., Enders 1995). For
example, we expect marketing effort to influence marketing
performance, and for some products, we expect both types
of variables to be non-stationary, e.g., in high-growth
markets. Hence, we expect marketing effort and marketing
performance to be cointegrated.
2.6. Estimation
We propose the use of standard VAR and Vector Error
Correction Models (VECM) to estimate the relationshipbetween the variables under investigation. If some variables
are non-stationary, but are not cointegrated, then one has to
difference them in order to make them stationary. Subse-
quently, we use these differenced transformed variables to
estimate a VAR. Further, if one has cointegrated variables,
one can estimate either a VAR in levels (i.e., with variables
that have not been differenced), or VECM (cf., Toda and
Yamada, 1996).
However, before estimating a VECM, we have to deter-
mine the cointegrating relationship that we can use as an
independent variable in the VECM. This relationship is a
linear combination of the cointegrating variable and is
stationary. Various estimation procedures, such as Johan-
sen's MLE, Box-Tiao, and OLS, are available to estimate
the rank of the cointegrating vector (which equals the
number of cointegrating vectors) and the cointegration
relationships. Typically, Johansen's MLE (we use this
method in our illustration) performs well with reasonable
large sample sizes (cf., Johansen, 1988; Hargreaves 1992).Once we have obtained the VAR and/or VECM parameter
estimates, we use these estimates to uncover the interactions
among the variables in the system. Specifically, we use
Granger causality, variance decomposition, and IRFs to
study the dynamic system.
2.7. Granger causality
We expect marketing effort to determine marketing
performance, in the words of time series literature, market-
ing effort Granger causes marketing performance. Often the
time paths of the two variables, marketing effort andmarketing performance, might show that the two variables
move together, e.g., both increase and decrease together. A
possible conclusion is that marketing effort is determining
marketing performance. However, one can also argue that
the firm is determining marketing effort based on marketing
performance. After all, constant advertising to sales ratio
strategies are quite common (Erickson, 1991). How do we
determine whether effort is determining performance, or
performance is determining effort, or both are determining
each other? Granger causality can help determine this.
2.8. Variance decomposition
The decomposition of forecast error variance throws light
on the effect size, i.e., how much of the forecast error
variance of the focal variable is being explained by the
variables of interests. For example, it helps to answer
questions like how much of forecast error variance of sales
is being explained by marketing effort and how much is
being explained by environmental variables.
2.9. Impulse response functions
After giving a shock to a particular variable in a system,
we use IRF to trace the time paths of all variables in thesystem. For instance, if we give a 10% shock to a firm's
advertising (in other words, we increase/decrease the firm's
advertising expenditure by 10%), we use IRFs to answer
questions such as: Does the shock to advertising have a
delayed effect on sales? How long does this effect last?
What is the likely effect on the sales of competitor's
product? What is the likely reaction of the competitor?
To sum, the last three steps of the nine-step framework
provide insights into the interactions between the variables
under investigation. They aid in understanding the influ-
ence of marketing effort and environment on marketing
performance and also help to uncover any feedback from
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performance to effort and/or environment. For the purpose
of illustrating the framework, we examine the famous case
of LPMC.
3. Research setting: the LPMC
We choose the LPMC to illustrate our methodological
framework for two reasons. Besides easy access, we choose
this database because two recent articles (Baghestani, 1991;
Zanias, 1994) have examined this database using cointegra-
tion analysis and we wanted to demonstrate that important
underlying dynamics of the market process may be missed if
one overlooks one or more of the steps of our framework
(e.g., structural breaks).
Palda (1964) provides a detailed review of the circum-
stances that led to the disclosure of advertising and sales
figures of LPMC. He also reviews the pertinent aspects of
the history of LPMC. This section first traces the relevantevents that throw light on the advertising strategy of LPMC
(drawing mainly from Palda, 1964).
The primary product (nearly 99% of sales) of LPMC was
a vegetable compound patented in 1873 alleged to cure a
wide variety of ills related to ``women's weakness.'' The
company relied solely on advertising as a means of promo-
tion (Palda, 1964), changing the advertising copy only three
times in the 54-year period. The aim of the advertising copy
was to stimulate primary demand (Palda, 1964). Of the three
advertising copy changes, two were due to orders issued by
governmental regulatory agencies. The first of the two copy
changes came about in November 1925 when the Food and
Drug Administration (FDA) issued a cease and desist order.
In 1938, the Federal Trade Commission had new objections
to the then existing form of advertising of LPMC, which
resulted in the second copy change in 1940. Winer (1979)
succinctly summarized the advertising copy positioning
strategy for LPMC as ``universal remedy'' for the period
19071914, ``relief for menstrual problems'' for the period
19151925, ``vegetable tonic'' for the period 19261940,
and ``universal remedy'' again, for the period 19401960.
In addition to these copy changes, LPMC followed an
aggressive advertising strategy under Lydia Gove, who took
over as director of the company in 1925. This streak of
aggressive advertising (which started in 1926) reached its peak in 1934 with advertising to sales ratio of 85%. The
then president of the company, Arthur Pinkham, took
objection to the huge expenditure on advertising, resulting
in a court case. This led to relatively lower levels of
advertising from 1936. Schmalensee (1972) estimated that
on average advertising was set at 64% of sales for the period
19261936, whereas it was around 46% of sales for the
other years.
The vegetable compound did not have any close sub-
stitute available for the time period (1907 1960) under
investigation, thereby ruling out any competitive advertising
effects (Palda, 1964). The price of the product, available in
tonic and tablet forms, was fairly stable over this time
period.3 Newspaper was the primary advertising medium
used by the company and the media allocation remained
fairly stable for the duration of the study.
The primary role of advertising in the marketing strategy
of LPMC, the lack of competitors, and the availability of
detailed data result in a rather unique natural experiment forstudying the advertising sales relationship, with minimal
variation in other variables (such as price, advertising
medium, etc.). The uniqueness of the LPMC experience
has led to an extensive literature analyzing the database.
Beginning with Palda (1964), who estimated the Koyck-
type distributed lag models using OLS, a host of researchers
have applied increasingly sophisticated time series methods
to study the LPMC data.4
Recently, Baghestani (1991) uses cointegration analysis
to investigate the advertisingsales relationship for LPMC.
He found that the advertising expenditure and sales figures
of LPMC are cointegrated in the order of one and, therefore,estimated an error correction model (ECM) to capture the
short-run dynamics and long-run equilibrium conditions.
Zanias (1994) replicated Baghestani's (1991) results and
went on to show that forecasting with an ECM was more
accurate in comparison to previous models. Further, Zanias
found bi-directional Granger-causality between sales and
advertising of LPMC.
Despite their state-of-the-art application of (Baghestani,
1991; Zanias, 1994) modern time series techniques, the
results from these bivariate cointegration analyses could be
misleading for the following two reasons. First, one cannot
be sure that the results do not suffer from bias due to omitted
variables, which could impact sales. In accordance with the
law of demand, price is one such variable. In addition, the
health of the economy is likely to influence demand and
thereby sales. In order to remedy the omitted variable bias
and to investigate the impact of price and the economic
environment on sales, we include GDP to capture the level of
economic activity and unemployment rate to utilize business
cycles in addition to advertising expenditure and price.
The second potential shortcoming, concerned with the
political legal environment, is that of the changes in
3 From 19151917, the price of the product in the liquid tonic form
and the tablet form was US$7.28 and was increased to US$9 and then
US$10 in 1918 and 1930, respectively. In May 1947, the price of the liquid
form of the product was increased to US$11 and then to US$12 in January
1948. The price for the tablet form of the product was increased to US$9.67
in June 1948, to US$10.30 on March 1956 and finally to US$11 in
November 1956 (see Palda, 1964, p. 39).4 These include Clarke and McCann (1973), Houston and Weiss
(1975), Caines et al. (1977), Helmer and Johansson (1977), Kyle (1978),
Weiss et al. (1978), Winer (1979), Hanssens (1980a), Mahajan et al., 1980,
Erickson (1981), Bretschneider et al. (1982), Harsharanjeet et al. (1982),
Heyse and Wei (1985), Magat et al. (1986). It is not our objective to survey
the entire stream of research that this database has generated. Our analysis
is based on two recent articles (Baghestani, 1991; Zanias, 1994), which
utilize the techniques we explicate in this paper.
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advertisement copy, which were required due to the regula-
tions by federal agencies, namely FDA and FCC. Resolu-
tions by such federal agencies are applied standards of what
the concerned agency conceives to be of public interest and
these resolutions reflect issues of not only politicallegal
nature but also reflect culturalsocial values (Palamountain,
1955). We expect these mandatory advertisement copychanges to influence the sales of LPMC and model these
as constraints imposed by the legal environment. This
surfaces in the statistical analysis in the form of structural
breaks in the parametric model estimated. In light of this,
we test for structural breaks and incorporate the detected
breaks into the cointegration analysis.5
4. Statistical analysis
In this section, we use cointegration analysis to examine
the impact of deflated GDP (RGDP), unemployment(UEMP), and deflated price (RPRICE) on both deflated
advertising (RAD) and sales (RSALES). In addition, we
investigate how advertising and sales influence each other in
the presence of these three variables. In the case of LPMC,
the price of the vegetable compound remained fairly stable
for the period under investigation, but the price in real terms
was changing. It is the price in real terms that truly reflects
the cost of a product; therefore, we use real price as an
explanatory variable.6 As the nominal price was fairly
stable, one could view RPRICE as instrumenting inflation-
ary pressures. To eliminate any spurious correlation due to
inflationary effects between advertising and sales and to
remain consistent across variables, we deflated both adver-
tising expenditure and sales revenue. The consumer price
index (base year 1967) was used to deflate advertising,
sales, and price, and the GDP deflator (base year 1967) was
used to deflate GDP.
4.1. Unit root tests
If a non-stationary time series yt can be made stationary
after differencing itdtimes, then yt is said to be integrated of
the orderd(denoted as yt$ I(d)). Tests suggested by Dickeyand Fuller (1981) and by Phillips and Perron (1988) are
recommended to test for the order of integration of time
series data.7 The augmented DickeyFuller (ADF) test, a
generalized form of the Dickey Fuller test, is useful for
testing for unit roots after incorporating appropriate lags.
The following ADF equation is estimated:
Dyt a0 yt1 ip
i2
biDyti1 4t 1
where is the coefficient of interest. If we fail to reject H0:
= 0, then the equation has a unit root, i.e., the underlying
data generating process is non-stationary. However, it is
possible that the equation has more than one root. Dickey
and Pantula (1987) suggest that one could use the Dickey
Fuller test recursively on successive differences of the
concerned variable to detect multiple roots. While using the
DickeyFuller tests, one must ensure that error terms are
uncorrelated and have constant variances. Phillips and
Perron (1988) developed a similar procedure to allow formilder assumptions about the distribution of the error
terms. Note that the null hypothesis of non-stationarity
forms the basis for both the Dickey Fuller test and the
PhillipsPerron test.
We utilize the Akaike Information Criterion (AIC) and
Bayesian Information Criterion (BIC) as fit statistics for
determining appropriate lag lengths. For RSALES and
UEMP, both AIC and BIC gave two lags as appropriate.
For the other three variables, there was no agreement
between the two criteria. As the goal is to find proper
relationships between variables, we took a conservative
perspective and used the maximum of the appropriate lag
length indicated by the two criteria.8 Hence, we use laglengths of three, four, and four for RAD, RPRICE, and
RGDP, respectively.
We present the results of the unit root tests in Table 1.
The results show that the five variables are all integrated of
order one, i.e., they are I(1), processes and, therefore, the
system seems appropriate for cointegration analysis.9 How-
ever, Perron (1989) found 14 macroeconomic time series to
be either stationary or trend-stationary after correcting for
structural breaks. In line with the evidence presented by
Perron (1989), we went about testing for structural breaks in
our five time series.
4.2. Structural break tests
For the LPMC, two possible events, besides the Great
Depression, are suggestive of structural breaks. The first
5 Note that we recognize that there is no way to be certain that one does
not have an omitted variable bias. However, when theory suggests that
specific variables are important (e.g., environment in the case of LPMC),
one should attempt to, at least, control for them. In the case of LPMC,
literature on marketing interactions suggests that we need to account for the
environment (cf., Wildt and Winer, 1983; Gatignon and Hanssens, 1987).
Based on this literature, we investigate the advertisingsales relationship
for LPMC and control for the environmental effects.
7 See Hamilton (1994) and Enders (1995) for thorough expositions.8 We estimated the concerned models with the lag lengths suggested by
both AIC and BIC and got results similar to those from the conservative
perspective.9 Nominal values of advertising (AD) and sales (SALES) were also
tested for unit roots. Like Baghestani (1991) and Zanias (1994), these two
series were found to be I(1).
6 The vegetable compound was available in two forms, namely tablet
and tonic. The price for both these forms was similar for most of the time
period under investigation (see Footnote 3). In our analysis, similar results
were obtained for both prices. For parsimony, we report results only for the
price of tonic.
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is the two advertising copy changes initiated by the
intervention of federal agencies. The first of these two
advertising copy changes came in 1925 due to a ceaseand desist from the FDA. The second copy change was
in 1940, when the FCC had objections to the existing
advertising copy of LPMC. The second potential struc-
tural break may result due to the streak of aggressive
advertising strategy followed from 1926 to 1936 by Lydia
Gove. We incorporate these structural breaks in our
analysis as suggestive of the interventions by the legal
environment. The years when LPMC had to change its
advertising copy due to federal regulations can be used as
suggestive of structural breaks in the advertising and
sales series.
Alternatively, some scholars suggest that one should let
the data determine the time of structural change (cf.,
Hansen, 1992). We followed Hansen's (1992) recommenda-
tions and found structural breaks in the advertising and sales
agreed with the dates suggested by the FDA and FCC
interventions. These findings support the conjectures con-
cerning the importance of the legal environment.
We used Hendry's (1989) version of the Chow test,
which relies on recursive updating of the residual sum of
squares to test for structural breaks. The test was per-
formed recursively for break in all time periods. Fig. 2
shows the plot of t-values for this recursive test. As is
evident from the figure, there were two breaks in both
advertising and sales. Advertising had structural breaks in1925 and 1934, while sales had structural breaks in 1925
and 1938. These dates agree with the advertising copy
changes due to federal regulation and Lydia Gove's ag-
gressive advertising strategy.
We also performed the recursive structural break test on
the other three variables. RPRICE had one structural break
in 1933, RGDP had two structural breaks in 1931 and 1938,
and UEMP had one structural break in 1930. As expected,
the Great Depression seems to influence the breaks in these
three variables. Subsequently, we used these structural
breaks in Perron's (1989) test for unit roots in the presence
of structural change.
4.3. Unit root with structural breaks tests
The Perron (1989) test for unit roots in the presence of a
structural break in period t incorporates structural change in
the period t = t + 1 and tests the following three null
hypotheses against the appropriate alternatives. The first
null hypothesis is of a one-time jump in the level of a unitroot process, and has the alternate of a one-time change in
the intercept of a trend-stationary process.
H1 : yt a0 yt1 m1DP 4t 2
A1 : yt a0 a2t m2DL 4t
where DP represents a pulse dummy variable. DP = 1 ift= t
+ 1; DP = 0 t T t + 1. DL represents the level dummyvariable and DL = 1, when t > t.
The second null hypothesis is of a permanent change in
the magnitude of the drift term vs. the alternate hypothesis
of a change in the slope of the trend.
H2 : yt a0 yt1 m2DL 4t 3
A2 : yt a0 a2t m3DT 4t
where DT represents a trend dummy. DT = t t, if t> t; DT= 0 if t t.
The third null hypothesis involves a change in both
the level and drift of a unit root process, and has the
alternate of a permanent change in level and slope of a
trend-stationary process.
H3 : yt a0 yt1 m1DP m2DL 4t 4
A3 : yt a0 a2t m2
DL m3
DT 4t
Perron (1989) provides t-statistics for testing each of
the above three hypotheses. These test statistics vary with
the ratio of time until the structural break to the total time
period under investigation. We conducted unit root tests
for the three hypotheses for each of the five variables in
our study (see Table 2 for results). RAD contained a unit
root, with its first difference, i.e., D1RAD, being trend-
stationary with one time change in the intercept.10
RSALES also contained a unit root with its first differ-
ence, i.e., D1RSALES, being trend-stationary with one
time change in the intercept. RPRICE contained a unit
root with its first difference, i.e., D1RPRICE, being trend-
stationary with permanent change in both the slope and
the intercept. Whereas, both RGDP and UEMP were trend-
stationary. RGDP was trend-stationary with permanent
change in both slope and intercept, whereas UEMP was
trend-stationary with one time change in the intercept.
10 Following standard convention in time series literature, we denote
the difference variables as Dn[Variable Name]. Thus, the first difference(i.e., n = 1) of RSALES would be D1RSALES and the second difference
would be D2RSALES.
Table 1
ADF and PP tests for unit roots
An intercept term was included in all the tests.
RAD RSALES RPRICE RGDP UEMP
ADFa 8.52 6.09 7.86 0.83 12.03ADF (trend)b 15.48 14.59 13.55 6.85 11.89
ADF (differenced)
a
707.75 170.81 26.11 248.95 269.55PPa 8.37 4.64 3.54 0.47 9.32PP (trend)b 11.36 7.61 5.94 7.34 9.25PP (differenced)a 36.15 32.53 35.99 36.15 26.91
a Critical values for ADF and PP at 5% level of significance is 15.7for OLS autoregressive coefficient (Hamilton, 1994).
b Critical values for ADF and PP at 5% level of significance is 22.4for OLS autoregressive coefficient (Hamilton, 1994).
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Fig. 2. Structural breaks in advertising and sales.
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To summarize, after incorporating structural changes,
there were three I(1) variables, namely RAD, RSALES,
and RPRICE and two trend-stationary variables, RGDP and
UEMP. Note that the finding concerning the two macro-
economic variables is consistent with that of Perron (1989).
4.4. Reconciling unit root tests before and after incorporat-
ing structural breaks
Our unit root tests showed all variables to be I(1)
processes, whereas after compensating for structural breaks
we find the three firm level variables, viz., advertising,
sales, and price, to be I(1) processes, but the two macro-
economic variables, GDP and unemployment to be trend-
stationary. To investigate all possible scenarios, we decided
to test model with five I(1) variables and a model with three
I(1) variables.
4.5. Cointegration tests
In general terms, if there exists a stationary linear
combination of two or more variables, all of which are
integrated of the same order, say d, i.e., they are all I(d),
such that this linear combination is integrated of orderI(dc), where c ! 1, then these variables are said to becointegrated. Cointegrated variables share a common sto-
chastic trend (Stock and Watson, 1988).11 Engle and Gran-
ger (1987) proposed a straightforward methodology to test
for cointegration. Let Xt be a vector of n variables all
integrated of order d, i.e., I(d). Estimate a vector A of size
n such that
AHXt et 5
If et is integrated of order d c, where c ! 1, then thevariables in the vector Xt are said to be cointegrated of
order c.
Baghestani (1991) and Zanias (1994) used the Engle and
Granger (1987) procedure to test for cointegration between
advertising and sales of LPMC, which are both I(1). Further,
they found the two variables to be cointegrated. Enders
(1995), among others, points out that the inherent weakness
of the Engle and Granger methodology is that it relies on a
two-step estimation procedure; as a result, the inferences for
the second step depend on which error term from the first
step is used in the second step. Thus, it is possible that
depending on the choice of the error term one could either
find the variables to be either cointegrated or not cointe-
grated. Enders (1995) recommends using Johansen's (1988)methodology, which relies on the relationship between the
rank of a matrix and its characteristic roots.
Johansen's method is a multivariate generalization of the
DickeyFuller unit root test. Eq. (6) depicts this general-
ization.
DXt A1 IXt1 4t 6
where Xt and 4t are the (n 1) vectors of variables anderrors, respectively, DXt represents Xt in first difference, AIis a (n n) matrix of parameters, and I is an (n n)identity matrix. The tests entail estimating the rank of (A1
I
), which equals the number of cointegrating vectors. In
Table 2
Unit root test with structural breaks
Variable Year of break L* t-statistic hypothesis 1 t-statistic hypothesis 2 t-statistic hypothesis 3
RAD 1925 0.35 1.79 2.64 3.17RAD 1934 0.52 1.80 2.59 3.61D1RAD 1925 0.35 3.61 3.61 3.90
D1RAD 1934 0.52 3.98a
3.62 3.93D2RAD 1925 0.35 5.67b 5.50b 5.69b
D2RAD 1934 0.52 5.53b 5.50b 5.45b
RSALES 1925 0.35 1.50 3.72 3.11RSALES 1938 0.59 2.26 3.17 3.09D1RSALES 1925 0.35 4.18c 3.79 4.32a
D1RSALES 1938 0.59 3.94a 3.83 3.89D2RSALES 1925 0.35 5.03b 4.92c 4.98b
D2RSALES 1938 0.59 4.76b 4.89b 4.70c
RPRICE 1933 0.50 0.11 2.83 0.03D1RPRICE 1933 0.50 3.34 3.30 4.39a
RGDP 1931 0.46 2.22 3.61 4.24a
RGDP 1938 0.59 2.11 3.71 3.91D1RGDP 1931 0.46 4.48b 4.58b 4.46a
D1RGDP 1938 0.59 4.95b 4.55c 4.90b
UEMP 1930 0.44 4.23c
2.89 4.59c
* L is computed as the number of years till present (i.e., test date) divided by the total number of years.a Significant at 1% level.
b Significant at 2.5% level.c Significant at 5% level.
11 See Hamilton (1994) and Enders (1995) for a thorough exposition of
issues relating to cointegration.
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practice, maximum likelihood estimation is used to obtain
these cointegrating vectors and the ltrace and lmax statistics
are used to test for the number of characteristics roots
different from unity, which gives us the number of
cointegrating vectors (Johansen and Juselius, 1990). These
tests rely on the ordering of the characteristic roots (li) and
Eq. (7) provides the estimates of these statistics for rcharacteristic roots.
ltracer Tn
ir1
ln1 li
lmaxrY r 1 Tln1 lr1 7
where li is the estimated value of the characteristic root
and T is the number of observations. The ltrace test has the
null hypothesis of the number of distinct cointegration
vectors being less than or equal to r against a general
alternative. The lmax statistic tests the null hypothesis that
there are r distinct cointegrating vectors against thealternative that there are r + 1 cointegrating vectors.
Johansen and Juselius (1990) have provided the critical
values for these statistics.
We estimated the ltrace and the lmax statistics for two
possible scenarios. First, after incorporating structural
breaks, we found the three micro time series (advertising,
sales, and price) to be I(1) and, therefore, we used these
three series as the non-stationary series. We present these
results in the top half of Table 3.12 As is evident from these
results, there is a possibility of one cointegrating vector, i.e.,
there exists one linear combination of these three variables
which is stationary.13 Second, tests on the data generation
process for the five variable system14 indicate the possibi-
lity of three cointegrating vectors (see the bottom half of
Table 3).15
To incorporate these findings of structural change and thecointegration between advertising, sales, and price, we
tested various specifications for the five variable system in
a VAR framework with error correction components
(VECM). Now we discuss these models.
4.6. VAR and ECM
VAR analysis is a symmetric simultaneous equation
system. In general, a VAR system can be written as:
Xt z i m
i 1
iXti Jt 8
where Xt is an n-vector of variables, Z is an n-vector of
constants, i is an n n matrix of coefficients, Jt is an n-vector of error terms, and m is the appropriate lag length. If
any of the variables are non-stationary, then it is possible to
difference or de-trend these variables before estimation to
make them stationary. If two or more variables are
cointegrated, then we include an error correction term (the
linear combination of the cointegrated variables which is
stationary) in the structural VAR analysis as an independent
variable, which gives us the appropriate VECM. A VECM
can then be written as
DXt z im
i1
iDXti Jt 9
where t1 is a vector of error correction components (i.e.,
the cointegrating vectors) and DXt is a vector of first
differences of the variables under investigation.
There has been a debate as to which of the above
specifications is appropriate. Until recently, the Johansen
approach was popular and was used to determine cointe-
grating relationship between variables under investigation.
Subsequently, one would rely on these tests to estimate a
VECM. However, recent works by Toda (1995), Toda and
12 The cointegration vector obtained by maximum likelihood estima-
tion is (see Johansen, 1988 for details): RAD0.473 RSALES37.062 RPRICE.
13 Though we find one cointegrating vector, it is not the same as that of
Baghestani (1991) and Zanias (1994). First, with n variables, there is a
possibility of finding n 1 cointegrating vectors. Thus, Baghestani (1991)and Zanias (1994) could have only gotten one cointegrating vector whereas
we could potentially get two or four (depending on the model) cointegrating
vectors. Further, the cointegration vector for Baghestani (1991) and Zanias
(1994) had two terms (i.e., advertising and sales) whereas the cointegrating
vector in our case has three (i.e., advertising, sales, and price) or five (i.e.,
advertising sales, price, GDP, and unemployment) terms.14 There is general agreement that the unemployment series is
stationary (cf., Perron, 1989). In the current data set, we found
unemployment to be integrated of order one. We conjectured that this
was due to the Great Depression years. Testing for structural breaks
indicated that there was one structural break in 1930. After correcting for
the break, as proposed by Perron (1989), unemployment was found to be
trend-stationary. Nevertheless, for the time period under consideration
unemployment is non-stationary.15 The cointegration vector obtained by maximum likelihood estima-
tion is: RAD 0.386 RSALES 2.333 RPRICE + 1.478 RGDP 13.682
UEMP.
tI
Table 3
Cointegration tests: Johansen's methodology
l Trace hypothesisal Trace
statistic
l Max
hypothesisal Max
statistic
Three-variable system
r 2, r > 2 0.98 r = 2, r = 3 0.98
r 1, r > 1 9.89 r = 1, r = 2 8.91r = 0, r > 0 43.78b r = 0, r = 1 33.89b
Five-variable system
r 4, r > 4 0.72 r = 4, r = 5 0.72r 3, r > 3 7.45 r = 3, r = 4 6.73r 2, r > 2 15.98 r = 2, r = 3 8.53r 1, r > 1 32.59 r = 1, r = 2 16.61
r 0, r > 0 75.88b r = 0, r = 1 43.29b
a Null hypothesis is stated first, then after the ` comma'' alternate
hypotheses is stated.b Significant at 1% level.c Significant at 5% level.
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Phillips (1993), Toda and Yamada (1996) and Phillips
(1995) have shown that this approach may not be reliable,
especially when less than 300 observations are available,
which is true in our case. Toda (1995) demonstrates that,
particularly with small data sets, inference concerning
Granger causality can be more reliable if drawn from a
VAR in levels form, because pre-test estimator biases are
avoided. There may be some inefficiency due to the need
to include enough lags to capture the non-stationary nature
of the data, but this is likely to be small in comparison to
the potential biases resulting from pre-testing (especially
since unit root and cointegration tests have been shown to
have low power for relatively small data sets).
In accordance with the above mentioned literature, we
adopt a pragmatic approach and consider inferences from
both a VAR in levels and from a VECM specified accord-ing to the results of preliminary unit root and Johansen
cointegration tests. The extent to which the results from
these approaches coincide will provide some indication of
the confidence with which we can draw conclusions from
the data.
Based on the above reasoning, we consider three
different configurations. First, is a VAR in levels with
the appropriate structural break for each of the five
variable system. Second, is a VECM with the cointegrat-
ing vector comprised of advertising, sales, and price, the
three variable found to be I(1) after incorporating appro-
priate structural breaks. Third, is a VECM with thecointegrating vector comprising the five variables. In the
remainder of the article, we refer to these models as
Models 1, 2, and 3, respectively.
Before estimating the ECMs, we tested each model for
the appropriate lag length (see Table 4 for results). As is
evident from the table, a lag length of 1 or 2 was appropriate
in most cases. In fact, we estimated the models with lag
length of either 1 or 2 and obtained similar results. For
parsimony, we report the results with lag length of 2.
4.7. Granger causality tests
The test for Granger causality in a VAR is to determine
whether the lags of one variable enter into the equation of
another variable. In the case of a VECM, where we have
cointegrated variables, Granger causality requires the addi-
tional condition that the speed of adjustment coefficient
Table 4
Lag length test
Here, we report AIC followed by BIC.
Model RAD RSALES RPRICE RGDP UEMP
Model 1: VAR with structural breaks in levels
Lag length 1 11.890 12.064 0.055 6.235 2.054
12.714
a
12.888
a
0.694
a
6.909 2.504Lag length 2 11.593 11.906a 0.282a 5.932a 1.843a
12.809 13.122 0.858 6.767a 2.451a
Lag length 3 11.458a,b 12.041 0.184 5.949 1.84613.078 13.660 1.358 6.952 2.617
Model 2: Three-variable cointegration
Lag length 1 10.844 12.077 0.035 6.244 2.03211.743a 12.976a 0.789a 6.993 2.631a
Lag length 2 10.581a 11.930a 0.312a 5.949a 1.87911.873 13.222 0.904 6.861a 2.638
Lag length 3 10.590 12.058 0.199 5.971 1.855a,b
12.286 13.754 1.420 7.051 2.781
Model 3: Five-variable cointegration
Lag length 1 10.126 11.994 0.033 6.247 2.08611.024a 12.893a 0.791a 6.996 2.686
Lag length 2 9.962a 11.915a 0.271a 5.944a 1.87911.254 13.206 0.944 6.856a 2.639a
Lag length 3 9.964 12.063 0.159 5.955 1.867a,b
11.659 13.759 1.459 7.034 2.793
a Optimal.b We checked for lag length of 4, but 3 was optimal.
Table 5
Granger causality
Model RAD RSALES RPRICE RGDP UEMP
A. Granger causality results: F-tests
Model 1: VAR with structural breaks in levels
RAD Granger caused 6.00
a
10.92
a
0.69 1.64 0.54RSALES Granger caused 2.12 7.46a 0.93 4.15b 2.34
Model 2: Three-variable cointegration
RAD Granger caused 20.01a 16.50a 12.43a 1.91 1.42
RSALES Granger caused 0.41 0.76 0.05 2.72c 1.96
Model 3: Five-variable cointegration
RAD Granger Caused 18.41a 15.09a 11.21a 11.36a 13.11a
RSALES Granger caused 1.19 1.57 0.81 2.72c 2.16
B. Granger causality: speed of adjustment coefficients
Model 2: Three-variable cointegration 1.287a 0.037 0.001 Model 3: Five-variable cointegration 1.365a 0.494 0.000 0.003 0.001
a p < 0.01.b
p < 0.05.c
p < 0.10.
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(beta coefficient of the cointegrating variable) to be different
from zero. We used the likelihood ratio test to verify
whether the lags of one variable enter into the equation of
another. We present the results for the three models in Table
5A and the results for the speed of adjustment coefficient for
the two VECMs (last two models) in Table 5B.
As is evident form Table 5A, for Model 1, the VAR inlevels, advertising is Granger caused by sales, whereas
sales is Granger caused by GDP. The results for the two
VECMs show that advertising is Granger caused by all the
variables in the cointegrating equation, i.e., sales and price
in Model 2 and sales, price, GDP, and unemployment in
Model 3. In addition, for Models 2 and 3, the speed of
adjustment coefficient is significant only for advertising. In
order to understand the size of the impact of the macro-
economic variables on sales and advertising we now turn
to decomposition of forecast error variance and IRF.
4.8. Variance decomposition and IRFs
Decomposition of the variances of the forecast error is
helpful in understanding the interrelationships amongst the
variables in the system. The forecast error variance decom-
position has information on the proportion of movement in a
series due to innovations in the series itself and innovations
in other series. IRFs demonstrate how one variable reacts to
a shock in another variable. Plotting the IRFs is a practical
way to visually represent the response in one series to a
shock in another series.
To compute variance decomposition and IRFs one must
write the VAR process in its equivalent Vector Moving
Average (VMA) form (Sims, 1980). That is, the VAR Eq.
(8) can be written in its equivalent VMA form16
Xt m I
i0
A4ti 10
The mechanics behind variance decomposition is straight-
forward. Taking the conditional expectation of Xt + 1 after
updating it by one period in Eq. (10) gives
EtXt1 a0 a1Xt 11
where a0 and a1 are estimated coefficients. We can subtract
the expected value from the actual value at period t + 1 toobtain a one-period-ahead forecast error. In a similar
manner, we can compute forecast errors for n periods in
the future. In the VMA form of the model, Eq. (10), the
second term on the right hand side gives the n forecast error,
i.e.,nIiH
0i4t + n i. Putting restrictions on the VAR system
decomposes the forecast error variance.
Both variance decomposition and IRFs are sensitive to
the ordering of variables in the VAR but the decomposition
of forecast error variance converges over time to the
unconditional variances. Table 6B displays the results from
the Choleski decomposition of the 40th period forecast error
variance for advertising and sales for the three models under
consideration. For Model 1, VAR in levels, advertising, and
salestaken togetheraccount for about 81% of forecast
error variance in advertising, whereas unemployment ex-
plains 11.9% of advertising forecast error variance. In sales,
74.51% of forecast error variance is explained by sales
itself, but the most important variable besides sales itself is
GDP. In fact GDP explains over two times the forecast error
variance explained by advertising, i.e., 12.47% vs. 6.19%.
As far as the three-variable cointegration model is con-
cerned (Model 2), advertising mainly explains itself
(64.99%) with GDP and unemployment together explaining
nearly 20% of forecast error variance in advertising. For
sales, besides sales itself, price (24.4%) seems to be the
most important variable. Here again, GDP and unemploy-
ment, taken together, explain more forecast error variance in
sales than advertising, i.e., 20.15% vs. 16.06%. For the five-
variable cointegration model, the results are similar to the
three variable cointegration model. Advertising (78.91%)
explains the bulk of its own forecast error variance, but the
second variable is GDP (13.99%). For sales, besides salesitself, we again find price (25.69%) to be the most important
variable. Again, the superiority of GDP over advertising in
explaining the forecast error variance in sales is demon-
strated (15.29% vs. 7.56%). We now discuss the IRFs.
The elements in the matrix A1i in Eq. (10) are called
impact multipliers. The impact multipliers, taken together,
form the IRF. We plotted the IRFs with upper and lower
90% confidence bounds obtained by Monte Carlo integra-
tion estimates of standard errors (see Doan, 1992 for
details). The IRFs were consistent across models. In Fig.
3, we present the IRFs of interestthe response of adver-
tising and sales to 10% shock. As is evident from these
16 Again, see Hamilton (1994) and Enders (1995) for details.
Table 6
Forecast error variance decompositionresults after 40 periods
All figures in this table are percentages.
Model RAD RSALES RPRICE RGDP UEMP
Model 1: VAR with structural breaks in levels
RAD variance
decomposition
35.24 46.71 4.34 1.80 11.90
RSALES variance
decomposition
6.19 74.51 3.63 12.47 3.20
Model 2: Three-variable cointegration
RAD variance
decomposition
64.99 6.21 8.63 9.89 10.28
RSALES variance
decomposition
16.06 39.39 24.40 13.39 6.76
Model 3: Five-variable cointegration
RAD variance
decomposition
78.91 0.51 4.22 13.99 2.36
RSALES variance
decomposition
7.56 46.03 25.69 15.29 5.42
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IRFs, a 10% shock to advertising results in sales instanta-
neously rising by about 9% with the effect dying out in
about two periods. A 10% shock to sales has a similar
impact on advertising.
4.9. Discussion
As in previous research (Baghestani, 1991; Zanias,
1994), we found advertising and sales to be integrated
Fig. 3. Impulse response functions of interest. (a) Model 2: shock to advertising response sales lag. (b) Model 2: shock sales response advertising lag. (c) Model
3: shock advertising response sales lag. (d) Model 3: shock sales response advertising lag.
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of order one. In addition, we find price, GDP, and
unemployment also to be integrated of order one. Further,
we find two structural breaks in both advertising and sales.
The structural breaks in advertising are in 1925 and 1934.
The first structural break coincides with the first federal
regulation against LPMC. The second break seems to be a
result of the depression and it appears that the impact of
depression took some years to set in. The two breaks in
sales were in 1925 and 1938. The break in 1925 coincided
with the first federal reprimand, whereas the second break
is at the end of the aggressive advertising streak by Lydia
Gove. We do not observe any impact of the second federal
intervention in 1940, perhaps, because the product had
already acquired a negative reputation. The one break in
Fig. 4. Time plots of advertising and sales.
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price is in 1930 and, as expected, coincides with the
great depression.
After incorporating structural breaks, the unit root tests
suggest that the order of integration of advertising, sales,
and price is the same. Even though the order of integration
of advertising and sales remain the same after incorporat-
ing structural breaks, the breaks alter the data generation process for the two series. This is evident from the time
plots of advertising and sales (Fig. 4) and is confirmed by
the Perron's (1989) test.
We identify one cointegrating vector, but this vector is
comprised of advertising, sales, and price and not advertis-
ing and sales as in previous research (Baghestani, 1991;
Zanias, 1994). Further, unlike the previous two research
endeavors, we find that advertising does not Granger cause
sales. It seems, at least in the case of LPMC, that the LPMC
executives determined the advertising levels by relying on
previous year's sales. However, advertising did not signifi-
cantly influence sales. Perhaps, this insight explains thesecond structural break in advertising. As the advertising
levels were based on sales, the advertising expenditure was
decreased when the depression had a significant influence
on sales. The variance decomposition results confirm the
weak effect of advertising on sales, as the environmental
variables explain more forecast error variance than advertis-
ing. The IRFs show that advertising does have a short-term
effect on sales, but the effect of sales on advertising is much
stronger. This leads more support to the thesis that advertis-
ing levels were determined based on sales.
5. Conclusion
Modeling of marketing interactions is important for
both marketing researchers and marketing practitioners.
With the growth in availability of single source data (cf.,
Curry, 1993) time series modeling is becoming more
important for both academicians and practitioners. We
borrow from the recent literature in time series on
multi-equation modeling to collate a set of econometric
tests and estimation techniques necessary for the use of
cointegration analysis. Cointegration analysis will aid inthe analysis of dynamic marketing interaction models and
help in uncovering the underlying dynamic process. The
framework provides guidelines as to the steps necessary
for the use of cointegration analysis.
Appendix A. Multi-equation model
where Aijk(L) is the polynomial in the lag operator L. We can write Eq. (A) as:
PE1 A APP AE1 E1 AE2 E2 AEE 4
where PE1 is the (p + e1) 1 vector of p performance variables and e1 endogenous effort variables; Pis the p 1 vector of performance variables; E1 is the e1 1 vector of endogenous effort variables; E2 is the e2 1 vector of exogenous effortvariables; Eis the e 1 vector of environmental variables; and 4is the (p + e1) 1 vector of error terms. Further, A is the (p +e1) 1 vector of constants; Ap is the (p + e1) p matrix of coefficients; AE
1is the (p + e1) e1 matrix of coefficients; AE2 is
the (p + e1) e2 matrix of coefficients; AE is the (p + e1) ematrix of coefficients.
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We illustrate the cointegration analysis for the famous
case of the LPMC. We show that recent research (Baghes-
tani, 1991; Zanias, 1994) had overlooked certain important
aspects of the analysis (e.g., structural break tests), which
resulted to their concluding bidirectional Granger causality,
whereas we found that advertising does not Granger cause
sales. In addition, our analysis uncovers the incidence andnature of extraneous environmental interventions. Future
research should use cointegration analysis to study the
advertising sales relationship in a competitive setting. Ques-
tions like: (1) which firm's (market leader or follower)
advertising spending follows the other; (2) what determines
the followers' advertising spendingfirms own sales or the
market leaders advertising spending, etc., can be easily
addressed by using cointegration analysis. In addition,
cointegration analysis can also be used to study other
dynamic situations like CEO compensation and the share
price of the firm's etc. Further, marketing practitioners will
find the framework handy, which is likely to in empiricalgeneralizations and advancement of marketing science.
Acknowledgments
A part of this paper was presented at the Marketing
Science Institute conference at Berkeley in April 1997.
The authors appreciate the helpful comments of Martin
S. Levy and Ravi Dharwadkar on the earlier versions of
this manuscript.
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