Using cointegration analysis for modeling marketing interactions in dynamic environments: methodological issues and an empirical illustration

8/9/2019 Using cointegration analysis for modeling marketing interactions in dynamic environments: methodological issues a

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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

Journal of Business Research 51 (2001) 127 144


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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.

R. Grewal et al. / Journal of Business Research 51 (2001) 127144128


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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.

R. Grewal et al. / Journal of Business Research 51 (2001) 127144 129


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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.



8/18

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).



9/18

Fig. 2. Structural breaks in advertising and sales.



10/18

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.



11/18

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.



12/18

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


A. Granger causality results: F-tests


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


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


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.



13/18

(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.



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


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


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



14/18

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.



15/18

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.



16/18

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.



17/18

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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Using cointegration analysis for modeling marketing interactions in dynamic environments: methodological issues and an empirical illustration