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

Journal of Business Research 51 (2001) 127 ± 144

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 a

Department of Marketing, Washington State University, Pullman, WA, 99164-4730 USA b 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., advertising, personal selling), and environmental conditions (e.g., growth rate, competitive activities). Typically, researchers use market response models to investigate marketing interactions 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 marketing interactions, scholars have proposed various methodological frameworks to model these interactions (cf., Wildt and Winer, 1983; Gatignon and Hanssens, 1987). Recent methodological advances in econometrics concerning cointegration 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. * Corresponding author. Tel.: +1-509-335-5848; fax: +1-509-3353865. E-mail address: [email protected] (R. Grewal).

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 analysis. 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 are cointegrated. Formally speaking, two or more non-stationary variables, which are integrated of the same order, are cointegrated if there exists a linear combination of these variables that is stationary. Specifically, cointegration analysis 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 example, such models have been used to study the interaction between the structure of marketing function (brand vs. category management) and competition (cf., Zenor, 1994;

0148-2963/01/$ ± see front matter D 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 competitive 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 Hanssens, 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. Hamilton, 1994; Enders, 1995). Typically, one differences nonstationary 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 nonstationary variables results in loss of information (cf., Enders, 1995). Cointegration analysis provides a methodology for analyzing non-stationary variables, without making them stationary, thereby preventing loss of information 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 instance, 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, cointegration analysis is a useful tool to examine sales force effectiveness (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 as mere illustrations of the usefulness of cointegration analysis in investigating marketing interactions. Marketing researchers are just beginning to use cointegration analysis to study marketing interactions. Specifically, 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 research on cointegration limits its use. Our primary objective 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 investigation is suitable for cointegration analysis. In addition, drawing conclusions from the estimation results of cointegration analysis requires more statistical tests. The main objective of this article is to demonstrate a comprehensive methodological framework for analyzing multi-equation time series data using cointegration analysis. Such a framework is of considerable interest to both marketing scientists and marketing managers, as better understanding of marketing 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 advancement 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 developments 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 Company (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 marketing performance into consideration. In addition, environment 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 expenditure this month which in turn influences sales. Multiequation 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 investigate the complex system represented in the two equations we present in Appendix A (Fig. 1). In the first four steps of the 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.

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Uncovering these aspects of the data generating mechanisms, provides information whether the variables being studied are suitable for cointegration analysis or not. Subsequently, 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 behavior 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 autocorrelation 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 (Dekimpe and Hanssens, 1995b). For example, the vast literature 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 examples 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 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.

structural breaks, like the exogenous oil price shock of 1973, most of the macroeconomic series are either stationary or trend-stationary. If a series is stationary or trendstationary, 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) demonstrated, overlooking structural breaks might mislead conclusions 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 highprofile (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, the structural 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 highprofile shocks, though this effect might be temporary. Interventions due to sales promotions or federal legislation'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.

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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 incorporating structural breaks is to overrule the possibility that a structural break may be causing misperceptions concerning the stationarity of the variables under study. Further, there exists 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 cointegrated. In such a case, we must proceed with the cointegration 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, cointegration 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.

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stationary. Various estimation procedures, such as Johansen'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, marketing effort Granger causes marketing performance. Often the time paths of the two variables, marketing effort and marketing 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.

2.6. Estimation

2.9. Impulse response functions

We propose the use of standard VAR and Vector Error Correction Models (VECM) to estimate the relationship between 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. Subsequently, 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 determine 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

After giving a shock to a particular variable in a system, we use IRF to trace the time paths of all variables in the system. 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 influence 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 cointegration 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 circumstances 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 relevant events 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 promotion (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 1907 ±1914, ``relief for menstrual problems'' for the period 1915 ±1925, ``vegetable tonic'' for the period 1926 ±1940, and ``universal remedy'' again, for the period 1940 ±1960. 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 1926 ±1936, whereas it was around 46% of sales for the other years. The vegetable compound did not have any close substitute 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 for studying 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 Koycktype 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 advertising± sales 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 1915 ± 1917, 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 regulations by federal agencies, namely FDA and FCC. Resolutions 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 political ± legal nature but also reflect cultural ± social values (Palamountain, 1955). We expect these mandatory advertisement copy changes 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 inflationary pressures. To eliminate any spurious correlation due to inflationary effects between advertising and sales and to remain consistent across variables, we deflated both advertising 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 it d times, then yt is said to be integrated of the order d (denoted as yt  I(d)). Tests suggested by Dickey and Fuller (1981) and by Phillips and Perron (1988) are

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recommended to test for the order of integration of time series data.7 The augmented Dickey ± Fuller (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 ˆ a0 ‡ ytÿ1 ‡

iˆp X iˆ2

bi Dytÿi‡1 ‡ "t

…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 Dickey± Fuller tests, one must ensure that error terms are uncorrelated and have constant variances. Phillips and Perron (1988) developed a similar procedure to allow for milder 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 Phillips ±Perron 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 lag lengths 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 However, 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

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 advertising ± sales relationship for LPMC and control for the environmental effects. 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.

For the LPMC, two possible events, besides the Great Depression, are suggestive of structural breaks. The first

7

See Hamilton (1994) and Enders (1995) for thorough expositions. 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). 8

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Table 1 ADF and PP tests for unit roots An intercept term was included in all the tests. ADFa ADF (trend)b ADF (differenced)a PPa PP (trend)b PP (differenced)a

4.3. Unit root with structural breaks tests

RAD

RSALES

RPRICE

RGDP

UEMP

ÿ8.52 ÿ15.48 707.75 ÿ8.37 ÿ11.36 ÿ36.15

ÿ6.09 ÿ14.59 170.81 ÿ4.64 ÿ7.61 ÿ32.53

ÿ7.86 ÿ13.55 ÿ26.11 ÿ3.54 ÿ5.94 ÿ35.99

0.83 ÿ6.85 248.95 0.47 ÿ7.34 ÿ36.15

ÿ12.03 ÿ11.89 269.55 ÿ9.32 ÿ9.25 ÿ26.91

a Critical values for ADF and PP at 5% level of significance is ÿ15.7 for OLS autoregressive coefficient (Hamilton, 1994). b Critical values for ADF and PP at 5% level of significance is ÿ22.4 for OLS autoregressive coefficient (Hamilton, 1994).

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 cease and 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 structural 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) recommendations 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 concerning 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 performed 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 in 1925 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 aggressive 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.

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 unit root process, and has the alternate of a one-time change in the intercept of a trend-stationary process. H1 : yt ˆ a0 ‡ ytÿ1 ‡ m1 DP ‡ "t

…2†

A1 : yt ˆ a0 ‡ a2 t ‡ m2 DL ‡ "t where DP represents a pulse dummy variable. DP = 1 if t = t + 1; DP = 0 t 6ˆ t + 1. DL represents the level dummy variable 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 ˆ a0 ‡ ytÿ1 ‡ m2 DL ‡ "t

…3†

A2 : yt ˆ a0 ‡ a2 t ‡ m3 DT ‡ "t where DT represents a trend dummy. DT = t ÿ 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 ˆ a0 ‡ ytÿ1 ‡ m1 DP ‡ m2 DL ‡ "t

…4†

A3 : yt ˆ a0 ‡ a2 t ‡ m2 DL ‡ m3 DT ‡ "t 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 trendstationary with one time change in the intercept.10 RSALES also contained a unit root with its first difference, 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 trendstationary with permanent change in both the slope and the intercept. Whereas, both RGDP and UEMP were trendstationary. 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[VariableÿName]. Thus, the first difference (i.e., n = 1) of RSALES would be D1RSALES and the second difference would be D2RSALES.

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Fig. 2. Structural breaks in advertising and sales.

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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 RAD D1RAD D1RAD D2RAD D2RAD RSALES RSALES D1RSALES D1RSALES D2RSALES D2RSALES RPRICE D1RPRICE RGDP RGDP D1RGDP D1RGDP UEMP

1925 1934 1925 1934 1925 1934 1925 1938 1925 1938 1925 1938 1933 1933 1931 1938 1931 1938 1930

0.35 0.52 0.35 0.52 0.35 0.52 0.35 0.59 0.35 0.59 0.35 0.59 0.50 0.50 0.46 0.59 0.46 0.59 0.44

ÿ1.79 ÿ1.80 ÿ3.61 ÿ3.98a ÿ5.67b ÿ5.53b ÿ1.50 ÿ2.26 ÿ4.18c ÿ3.94a ÿ5.03b ÿ4.76b ÿ0.11 ÿ3.34 ÿ2.22 ÿ2.11 ÿ4.48b ÿ4.95b ÿ4.23c

ÿ2.64 ÿ2.59 ÿ3.61 ÿ3.62 ÿ5.50b ÿ5.50b ÿ3.72 ÿ3.17 ÿ3.79 ÿ3.83 ÿ4.92c ÿ4.89b ÿ2.83 ÿ3.30 ÿ3.61 ÿ3.71 ÿ4.58b ÿ4.55c ÿ2.89

ÿ3.17 ÿ3.61 ÿ3.90 ÿ3.93 ÿ5.69b ÿ5.45b ÿ3.11 ÿ3.09 ÿ4.32a ÿ3.89 ÿ4.98b ÿ4.70c ÿ0.03 ÿ4.39a ÿ4.24a ÿ3.91 ÿ4.46a ÿ4.90b ÿ4.59c

* 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.

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 macroeconomic variables is consistent with that of Perron (1989). 4.4. Reconciling unit root tests before and after incorporating 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 macroeconomic variables, GDP and unemployment to be trendstationary. 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 order I(d ÿ c), where c  1, then these variables are said to be cointegrated. Cointegrated variables share a common stochastic trend (Stock and Watson, 1988).11 Engle and Granger (1987) proposed a straightforward methodology to test

11 See Hamilton (1994) and Enders (1995) for a thorough exposition of issues relating to cointegration.

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 A0 Xt ˆ et

…5†

If et is integrated of order d ÿ c, where c  1, then the variables 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 cointegrated. 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 Dickey± Fuller unit root test. Eq. (6) depicts this generalization. DXt ˆ …A1 ÿ I†Xtÿ1 ‡ "t

…6†

where Xt and "t are the (n  1) vectors of variables and errors, respectively, DXt represents Xt in first difference, AI is a (n  n) matrix of parameters, and I is an (n  n) identity matrix. The tests entail estimating the rank of (A1 ÿ I ), which equals the number of cointegrating vectors. In

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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 r characteristic roots. ltrace …r† ˆ ÿT

n X

ln…1 ÿ ^li †

iˆr‡1

lmax …r; r ‡ 1† ˆ ÿT ln…1 ÿ ^lr‡1 †

…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 the alternative 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 possibility of three cointegrating vectors (see the bottom half of Table 3).15

12 The cointegration vector obtained by maximum likelihood estimation is (see Johansen, 1988 for details): RADÿ0.473  RSALESÿ37.062  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 ÿ 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 estimation is: RAD ÿ 0.386  RSALES ÿ 2.333  RPRICE + 1.478  RGDP ÿ 13.682  UEMP.

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Table 3 Cointegration tests: Johansen's methodology l Trace hypothesisa

l Trace statistic

l Max hypothesisa

l Max statistic

Three-variable system r  2, r > 2 r  1, r > 1 r = 0, r > 0

0.98 9.89 43.78b

r = 2, r = 3 r = 1, r = 2 r = 0, r = 1

0.98 8.91 33.89b

Five-variable system r  4, r > 4 r  3, r > 3 r  2, r > 2 r  1, r > 1 r  0, r > 0

0.72 7.45 15.98 32.59 75.88b

r r r r r

0.72 6.73 8.53 16.61 43.29b

= = = = =

4, 3, 2, 1, 0,

r r r r r

= = = = =

5 4 3 2 1

a

Null hypothesis is stated first, then after the ``comma'' alternate hypotheses is stated. b Significant at 1% level. c Significant at 5% level.

To incorporate these findings of structural change and the cointegration 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 ˆ z ‡

iX ˆm iˆ1

i Xtÿi ‡ 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 nvector 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 ^ tÿ1 ‡ DXt ˆ z ‡ 

iˆm X iˆ1

i DXtÿi ‡ Jt

…9†

where tÿ1 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 cointegrating relationship between variables under investigation. Subsequently, one would rely on these tests to estimate a VECM. However, recent works by Toda (1995), Toda and

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Table 4 Lag length test Here, we report AIC followed by BIC. Model

RPRICE

RGDP

UEMP

Model 1: VAR with structural breaks in levels Lag length 1 11.890 12.064 ÿ0.055 12.714a 12.888a 0.694a Lag length 2 11.593 11.906a ÿ0.282a 12.809 13.122 0.858 Lag length 3 11.458a,b 12.041 ÿ0.184 13.078 13.660 1.358

6.235 6.909 5.932a 6.767a 5.949 6.952

2.054 2.504 1.843a 2.451a 1.846 2.617

Model 2: Three-variable cointegration Lag length 1 10.844 12.077 11.743a 12.976a Lag length 2 10.581a 11.930a 11.873 13.222 Lag length 3 10.590 12.058 12.286 13.754

ÿ0.035 0.789a ÿ0.312a 0.904 ÿ0.199 1.420

6.244 6.993 5.949a 6.861a 5.971 7.051

2.032 2.631a 1.879 2.638 1.855a,b 2.781

Model 3: Five-variable cointegration Lag length 1 10.126 11.994 11.024a 12.893a Lag length 2 9.962a 11.915a 11.254 13.206 Lag length 3 9.964 12.063 11.659 13.759

ÿ0.033 0.791a ÿ0.271a 0.944 ÿ0.159 1.459

6.247 6.996 5.944a 6.856a 5.955 7.034

2.086 2.686 1.879 2.639a 1.867a,b 2.793

a b

RAD

RSALES

Optimal. We checked for lag length of 4, but 3 was optimal.

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 according 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 cointegrating vector comprised of advertising, sales, and price, the three variable found to be I(1) after incorporating appropriate structural breaks. Third, is a VECM with the cointegrating 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 additional condition that the speed of adjustment coefficient

Table 5 Granger causality Model A. Granger causality results: F-tests Model 1: VAR with structural breaks in levels RAD Granger caused RSALES Granger caused Model 2: Three-variable cointegration RAD Granger caused RSALES Granger caused Model 3: Five-variable cointegration RAD Granger Caused RSALES Granger caused B. Granger causality: speed of adjustment coefficients Model 2: Three-variable cointegration Model 3: Five-variable cointegration a b c

p < 0.01. p < 0.05. p < 0.10.

RAD

RSALES

RPRICE

RGDP

UEMP

6.00a 2.12

10.92a 7.46a

0.69 0.93

1.64 4.15b

0.54 2.34

20.01a 0.41

16.50a 0.76

12.43a 0.05

1.91 2.72c

1.42 1.96

18.41a 1.19

15.09a 1.57

11.21a 0.81

11.36a 2.72c

13.11a 2.16

ÿ1.287a ÿ1.365a

ÿ0.037 ÿ0.494

0.001 0.000

± 0.003

± 0.001

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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 in levels, 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 macroeconomic 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 decomposition 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 ˆ m ‡

1 X

A"tÿi

…10†

iˆ0

The mechanics behind variance decomposition is straightforward. Taking the conditional expectation of Xt + 1 after updating it by one period in Eq. (10) gives Et …Xt‡1 † ˆ a0 ‡ a1 Xt

…11†

where a0 and a1 are estimated coefficients. We can subtract the expected value from the actual value at period t + 1 to obtain 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, nÿ1 P i"t + n ÿ i. Putting restrictions on the VAR system i.e., iˆ0 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 16

Again, see Hamilton (1994) and Enders (1995) for details.

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Table 6 Forecast error variance decomposition Ð results after 40 periods All figures in this table are percentages. Model

RAD

RSALES

RPRICE

RGDP

UEMP

1.80

11.90

12.47

3.20

8.63

9.89

10.28

24.40

13.39

6.76

4.22

13.99

2.36

25.69

15.29

5.42

Model 1: VAR with structural breaks in levels RAD variance 35.24 46.71 4.34 decomposition RSALES variance 6.19 74.51 3.63 decomposition Model 2: Three-variable cointegration RAD variance 64.99 6.21 decomposition RSALES variance 16.06 39.39 decomposition Model 3: Five-variable cointegration RAD variance 78.91 0.51 decomposition RSALES variance 7.56 46.03 decomposition

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 salesÐtaken togetherÐaccount for about 81% of forecast error variance in advertising, whereas unemployment explains 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 concerned (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 unemployment, taken together, explain more forecast error variance in sales than advertising, i.e., 20.15% vs. 16.06%. For the fivevariable 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 sales itself, 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 demonstrated (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 integration estimates of standard errors (see Doan, 1992 for details). The IRFs were consistent across models. In Fig. 3, we present the IRFs of interestÐthe response of advertising and sales to 10% shock. As is evident from these

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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.

IRFs, a 10% shock to advertising results in sales instantaneously 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

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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

141

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 incorporating 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 advertising 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 significantly influence sales. Perhaps, this insight explains the second 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 advertising. 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 advertising 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 in the 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 ˆ A ‡ AP P ‡ AE 1 E1 ‡ AE 2 E2 ‡ AE E ‡ " where PE1 is the ( p + e1)  1 vector of pperformance 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 effort variables; E is the e  1 vector of environmental variables; and "is 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; AE1 is the ( p + e1)  e1 matrix of coefficients; AE2 is the ( p + e1)  e2 matrix of coefficients; AE is the ( p + e1)  ematrix of coefficients.

R. Grewal et al. / Journal of Business Research 51 (2001) 127±144

We illustrate the cointegration analysis for the famous case of the LPMC. We show that recent research (Baghestani, 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 and nature of extraneous environmental interventions. Future research should use cointegration analysis to study the advertising sales relationship in a competitive setting. Questions like: (1) which firm's (market leader or follower) advertising spending follows the other; (2) what determines the followers' advertising spending Ðfirms 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 empirical generalizations and advancement of marketing science.

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