Cointegration analysis of the aggregate advertising-consumption relationship.

ABSTRACT

This paper examines the relationship between advertising and consumption at the aggregate level In applying unit root tests and cointegration analysis to the annual U.S. data on advertising, personal consumption, and disposable personal income, we found that aggregate advertising, personal consumption, and disposable personal income from 1929 to 1997 are cointegrated with one cointegrating vector. That is, there is a long term equilibrium relationship among them. Also, the logged values of these variables were found cointegrated with one vector. The results show that advertising was negatively related to disposable personal income. The findings also indicate that advertising elasticity was low, which supports the basic findings at the micro level Several forms of causal tests were conducted to make causal inferences on the relationships among the variables. Managerial and research implications of the findings are also discussed.

1. INTRODUCTION

In the marketing literature, the relationship between advertising and sales at the individual firm and industry level has been a hotly debated issue for decades. The central question is whether or not advertising has current and/or future (or "carry over") effects on sales. A number of studies examined the advertising-sales relationship at the micro level (e.g., Bass and Parsons, 1969; Clarke, 1976; Deighton et al., 1994; Weinberg and Weiss, 1982; Weiss and Windal, 1980). However, the advertising-sales relationship at the macro or aggregate level has not gained much attention.

Corresponding to the advertising-sales link at the micro level, the relationship of its kind at the macro level is between aggregate advertising and consumption at the national level, which can be considered a domain of macromarketing. For example, Wilkie and Moore (1999) discuss the fundamental contributions marketing has to offer to humanity and civilization.

The principal purpose of this paper is to uncover the advertising-consumption relationship at the macro level by using the aggregate U.S. data with the aid of cointegration analysis. The organization of the paper is as follows: a brief overview of relevant studies is conducted, followed by a succinct exposition of the methodology utilized in the investigation. The paper continues with the results presentation and discussion. In the end, the paper finishes with concluding remarks.

2. BACKGROUND

The marketing literature has a rich tradition in sales-advertising research. However, the effects of advertising on sales are still not unequivocally clear. While advertising has an immediate impact on sales, it also generates sales during the subsequently short time periods after advertising has stopped, which is called the "short-run carryover effects" by Aaker and Carman (1982), or "cumulative" or "lagged effects" by Palda (1965). After an extensive study on cumulative advertising effects using the Koyck models, Palda avowed that "the measurement of cumulative advertising effects can be successfully attempted with the help of Koyck's model of distributed lags" (p. 179). He further concluded that the evidence for supporting the existence of lagged effects of advertising was clear. However, according to Bass and Clarke (1972), nonmonotonic lag distributed models may be preferred to the restrictive Koyck model for studying the sales-advertising relationship. In the presence of lag effects, maximum likelihood methods would be more appropriate than ordinary least squares (OLS).

A number of early studies on the sales-advertising relationship were based on the Koyck or more general distributed lag models. The major concern with this approach is that the possible reciprocal causality relationship is ignored. Distributed lag models treat advertising as an exogenous variable and sales as a dependent variable. However, in reality this assumption is problematic in that marketing managers often spend a certain percentage of projected sales on advertising. In other words, advertising budgets and sales are mutually dependent; as such, advertising may not be considered as exogenous. Therefore, if we continue to use distributed lag models, the Hausman specification error test (Hausman, 1976) must be employed for detecting the simultaneity problem.

As researchers tried to estimate the effects of advertising on sales, the controversy over methodological issues continued (Hanssens et al., 1990). As a result, the "real" effects, if there are any, advertising may have on sales is a point of enduring contention. While some studies did not find any significant relationship between advertising and sales (Tellis, 1988a), other studies found a significant relationship between the two (e.g., Deighton et al., 1994). Using a meta-analysis method, Assmus et al. (1984) found that advertising elasticity is 0.22, which indicates that the effects of advertising on sales are small.

In a recent article, Tellis et al. (2000) utilized a general distributed lag modeling approach to estimate the effects of direct television advertising on a toll-free referral service. Using highly disaggregate data at the hourly level, they found that ads have current and short term carryover effects on the number of referral calls. If the advertising budget is independent of referral calls, their approach is justified.

Long ago, Dhalla (1978) pointed out that since advertising has a long term effect on sales, sales must be treated as a capital investment. A more recent study expressed a similar point of view (Jedidi et al., 1999). However, due to the complexity of the issue and the controversy over the methodology used in the early studies, more research is needed regarding the sales-advertising relationship before any drastic action can be taken.

Although the advertising-sales study at the micro level is an issue of long-lasting interest, we are not pursuing it here. Instead, we focus on its corresponding relationship at the macro level between aggregate advertising and consumption, since aggregate consumption at the macro level is a proxy for sales at the micro level. Thus, we are investigating the aggregate advertising-consumption link at the US national level. According to Little (1979), macro or aggregate models are crucial in confirming micro models. Results from micro models that use data at the firm, industry, or consumer level must reproduce the empirical macro effects that are based on the aggregate data. For example, Baghestani (1991) has applied the cointegration technique to the annual Lydia Pinkham advertising and sales data documented by Palda (1965). Bahestani revealed bi-directional causations between advertising and sales, an interesting finding which previous studies using the traditional methodologies were unable to detect. The question that can be asked is whether the finding holds true at the national level.

As the macromarketing level, there are some unique problems that need to be addressed. For example, advertising has been blamed for promoting spending and creating artificial needs and wants among consumers (e.g., Galbraith, 1967). Issues of this magnitude must be investigated at the aggregate level. At the micro level, i.e., the firm level, some ads work, and others do not. For example, Lodish et al. (1995) found that only half of the ads examined worked. If an ad does not work, promoting spending is a non-issue. Thus, whether advertising promotes spending cannot be evaluated at the micro level. Rather, we want to know whether, on average, advertising has an effect on consumption or not. Thus, this accusation can be resolved only by inspecting the aggregate advertising-consumption relationship. In fact, some studies have been done on this line of inquiry. While some researchers (e.g., Quarles and Jeffres, 1983; Taylor and Weiserbs, 1972) did not find any positive influence advertising had on consumption, others (e.g., Jacobson and Nicosia, 1981; Peel, 1975) obtained evidence in support of advertising affecting consumption. In the economics literature, there was a huge debate on the relationship between aggregate consumption and advertising. Based on Schmalensee (1972) and others' studies, Berndt (1991) stated that it is safe to say that aggregate consumption has an impact on aggregate advertising, not vice versa. Yet he called for more study on the matter using new econometric methods before the controversy could finally be settled.

Due to the contention and seriousness of the issue, the need to re-examine the issue is imperative. Furthermore, this study can shed light on some of the benefits marketers claim aggregate marketing systems provide to society. According to Wilkie and Moore (1999), employment and personal incomes are among the top contributions marketing makes to the economic system. In fact, using the UK data, Chowdhury (1994) discovered that advertising has a negative causal impact on the employment rate. We will include personal income in our study to explore the other half of their statement. In addition, we will investigate the long term advertising elasticity on consumption at the aggregate level. Some causal tests will be employed to throw insights into the causal (a loaded word) relationships among advertising, consumption, and personal income. We hope to open up a stream of empirical research in macromarketing and at the same time build a bridge to connect with the micro phenomena. Next, we turn to a succinct exposition on the unit root and cointegration tests utilized in this study. More information on these techniques can be found in Dekimpe and Hanssens (1995a, b).

3. TESTING FOR UNIT ROOT AND COINTEGRATION

The concept of spurious regression (Granger and Newbold, 1974) specifies that statistical results look fabulous, but they do not endure. Spurious regression is a serious problem for time series analysis. The reason is that many time series tend to exhibit a similar trend, such as an increase in value over time. Thus, they seem correlated, but in fact they may not be. To avoid this pitfall, unit root tests and cointegration analysis can be helpful.

Theory suggests that certain pairs of time series variables may trend together. They may diverge from each other every now and then, but in the long run they converge to a common trend by the underlying market mechanism and/or policy decisions. The common trend is of great interest to researchers and may be discovered by a cointegration test (Engle and Granger, 1987; Granger, 1981, 1986).

A time series, [X.sub.t] is said to be stationary if its mean, variance, and covariance exist and they are invariant to time t. On the other hand, a nonstationary time series possesses characteristics that are a function of time t. However, a nonstationary time series can always be transformed to be stationary if we take the difference between the values of the two successive periods. The time series, [X.sub.t], is said to be integrated of order d (denoted [X.sub.t] ~ I(d)) if it becomes a stationary series after differencing d times (Engle and Granger, 1987). A Dickey-Fuller (DF) test (Dickey and Fuller, 1979, 1981) is often used for establishing the order of integration of the series. The DF equation

(1) [X.sub.t] - [X.sub.t-1] = [DELTA][X.sub.t] = a + bt + c[X.sub.t-1] + [e.sub.t]

tests the null hypothesis of a unit root, c = 0, which is equivalent to nonstationary, and the alternative hypothesis is that the series is stationary. We use [DELTA] to represent the difference of the series. The augmented Dickey-Fuller (ADF) equation

(2) [X.sub.t] - [X.sub.t-1] = [DELTA][X.sub.t] = a + bt + c[X.sub.T-1] + [[summation].sub.j] [d.sub.j] ([X.sub.t.j] - [X.sub.t-j-1]) + [e.sub.t]

is employed with j taking values from 1 to k and k is chosen to ensure that e is white noise. White noise means that the series has zero mean, constant variance, and no autocorrelation. The null hypothesis is still c = 0, a unit root in X. The ADF test statistics have the same asymptotic distribution as the DF statistics. Thus, the same critical values reported in Fuller (1976) can be used.

When a system of nonstationary time series is integrated of the same order, and one linear combination of them is stationary, they are considered cointegrated. This linear combination is the long term relationship among these nonstationary time series, which may be due to market mechanisms and/or policy decisions, and is the issue of interest.

A system of equations for n number of nonstationary variables with the same order can expressed as follows:

(3) [Y.sub.t] - [Y.sub.t-i] = [DELTA][Y.sub.t] = u + [[summation].sub.i] [[GAMMA].sub.l] [DELTA][Y.sub.t-i] + [PHI][Y.sub.t-p] + [[epsilon].sub.t]

where [Y.sub.t] is an n x 1 vector of the variables under investigation, u represents constants of an n x 1 vector, and i takes value from 1 to p-1. The rank of [PI], which is an n x n matrix, determines the cointegration properties of the system (Johansen, 1988, 1991; Johansen and Juselius, 1990). If [PI] has a rank of zero, these time series are not cointegrated since there is no linear combination that can make the system stationary. If the rank is r, which is less than n, there will be r possible linear combinations that can achieve stationarity for the system of variables. If r is equal to n, all the series are stationary, in which case, cointegration is a non-issue. We now turn to the results discussion.

4. EMPIRICAL RESULTS

For this study, we collected the data in millions of dollars on aggregate annual personal consumption, advertising, and disposable personal income for the U.S. from 1929 to 1997 from various issues of Statistical Abstract of the United States and Survey of Current Business. Quarterly data would have been preferred to annual data. Unfortunately, advertising data are compiled only on a yearly basis. Annual consumption is a summation of expenditures on durables, nondurables, and services. We noticed that promotional expenses, other than advertising, really have picked up in past ten years. For example, manufacturers increased their consumer and trade promotional expenses from 50% to 75% of marketing budgets during the 1985-90 time period (Forbes, 1991). However, data on promotions are hard to find and have a short history and thus could not be included in the study. As such, in anticipation of a surge in popularity of using promotions in the 1990s, we estimated our model based on the data from 1929 to 1997. There are some good reasons for selecting this period for our inquiry. Based on a meta- analysis, Tellis (1988b) found that the price elasticity is eight times larger than the advertising elasticity found by Assmus et al. (1984). To maintain its comparability in terms of time frame, the selected period can lend our results credibility to make a comparison to the micro findings. Although the central issue is to probe the relationship between aggregate advertising and consumption, we also included disposable personal income because it affects consumption. We transformed the data into the real data by the GDP price deflator, and did our analysis with the real data. Thus, all the variables are in constant dollars, not current dollars.

To make sure that the three time series are integrated of the same order, we conducted the DF and ADF tests. While we included an intercept and t term in the DF and ADF tests for the original series, the unit root tests for the difference of the series dropped the term t because the original series display an obvious upward moving trend. For the ADF test, we used the general-to-specific and the specific-to-general approaches to select the optimal lag length. The largest lag length is determined by taking the integer part of {12 x [(m/100).sup.0.25] + 2} (Schwert, 1987), where in is the number of observations in the series, which is 62. Thus, the largest lag length for our study is 12. That is, k in equation 2 is 12. The results of DF and ADF tests are given in Table 1.

For simplicity, we denote the advertising, consumption, and disposable personal income series by AD, CON, and DPI, respectively, the difference of the series for advertising, consumption, and disposable personal income by AAD, ACON, and ADPI, respectively. Although there are some conflicting results between the DF and ADF tests, which is not uncommon (e.g., Bronnenberg et al., 2000), we believe that all the variables are integrated of order 1, I(1), as most economic variables are. That is, the three series are nonstationary, but achieve stationarity after differencing once, which is supported by the chi-square test for stationarity (shown in Table 2).

Since the series are integrated of the same order, we conducted a cointegration analysis. We employ the Johasen and Juselius (JJ) procedure (1988, 1990) for testing whether the series are cointegrated. That is, it is to test whether one or multiple linear combination(s) of them will achieve stationarity. For instance, if the rank of [PHI] in equation (3), r, is 1, there is a single cointegrating vector. That is, there is only one linear combination. If r = 0, the series are not cointegrated.

That is, there is no long term relationship among the series. The rank, r, is formally assessed with two tests. The maximum eigenvalue test has the null hypothesis of r [less than or equal to] g, and the alternative hypothesis is r = g + 1. The trace test has the same null hypothesis, r [less than or equal to] g, but a slightly different alternative hypothesis, r [greater than or equal to] g + 1. Both statistics show that AD, CON, and DPI are cointegrated with one cointegrating vector, which is supported by the chi-square test for exclusion, indicating that all the variables must be included in the cointegrating vector. The results are reported in Table 2.

Since AD, DPI, and CON are cointegrated, we can examine their cointegrating vector, which reveals the long term relationship among them. For the same vector, we can normalize different variables so that we get three distinctive normalized equations, but the underlying relationship is the same. Since the variables are cointegrated, OLS regression could be used as a benchmark. The estimated R square is close to 1. As we see some differences between the relationship among the three variables as reflected in the cointegrating vector and as revealed in the regular regressions, we stay with the cointegration results. The cointegration analysis has advantage over the regression analysis in that the former treats all the variables with the same status.

That is, the former does not specify dependent and independent variables, whereas the latter does. Thus, we report only the cointegration results in Table 3. In order to calculate advertising elasticity, we take the log values of these variables and repeat the cointegration analysis. The results show that the logged values of these variables are also nonstationary and cointegrated of order 1. The cointegrating equations for the logged form are in Table 4.

While the cointegration vector tells us the relationship among the cointegrating variables, the vector does not say anything about the causal relationship among the variables. To shed light on the causality issue, we conducted Granger causality tests.

According to Granger (1969), if the lagged value of X will help explain the current value of Y while accounting for the lagged value of Y, X has a causal impact on Y in Granger sense. In other words, if the lagged value of X and Y will present a stronger predictive power in explaining the current value of Y than the lagged value of Y alone, X causally influences Y. The results show that during the period studied, while CON and DPI had causal impact on AD, AD had no such effect on either CON or DPI. CON had a causal influence on DPI, not vice versa. We also conducted Geweke-Meese-Dent (GMD) test (1982), which is similar to Granger test in theory, but is implemented differently. With GMD test, if the future value of X is helpful in explaining the current value of Y while accounting for the lagged value of Y and lagged value of X as well as current value of X, X is said to have a causal impact on Y. Interestingly or surprisingly, the only significant result is that AD had a causal impact on consumption at the 10% level. The results are reported in Tables 5 and 6.

5. DISCUSSION

The cointegration analysis indicates that, from 1929 to 1997, as CON increased by $1, DPI would increase by $1.255. On the other hand, as DPI increased by $1, CON would increase by $0.797, which is the marginal propensity to consume (MPC). This finding supports Keynes's (1936) celebrated theory of the consumption function. Keynes stated that increase in consumption is proportional to increase in income. That is, as income increases, people tend to spend more within constraint. In other words, people will spend a fraction of the increased income, not all of it, which means MPC must be smaller than 1 and larger than 0. Since our above result is in accordance with the well known hypothesis, it increases our confidence in the study. The results also indicate that as CON increased by $1, so would AD increase by $ 0.209. As AD increased by $1, CON would increase $4.774.

However, the surprising finding is that AD and DPI moved in opposite directions. An increase in DPI would decrease AD, and a raise in AD would reduce DPI. That is, advertising expenditures were negatively related to personal income. The reason for this negative effect of advertising on personal income is unknown, although the finding itself is not totally out of blue. In fact, using aggregate data from the UK, Chowdhury (1994) found that advertising expenditures had a strong negative uni-directional causal impact on the employment rate.

The cointegrating equations from the logged form enable us to discuss the relationships among the variables in terms of elasticity. The long term advertising elasticity is 0.181, which is comparable to 0.22, the mean elasticity of advertising found by Assmus et al. (1984) using meta-analysis. As Tellis (1988b) claimed, 0.22 could be biased upward due to method problems. Our result seemingly supports his assertion. As Tellis (1988b) found, the mean of price elasticity (-1.76) is eight times larger than the average elasticity of advertising. This finding points out that advertising has a milder effect on sales in comparison to price reduction, which may help us understand why in the past decade, promotional activities other than advertising have become so popular.

In the past decade, while advertising spending as a proportion of the total outlays of sales promotion has been decreasing, promotional expenditures in the form of coupons, features, and displays have been increasing. For example, companies spent an average of 42 percent of total promotional budgets on media advertising in 1977, and the percentage dropped to 26.5 by 1994 (Donnelly Marketing Inc., 1995). Consumer packaged good manufacturers paid out half of the $70 billion promotional budget on trade promotion (Progressive Grover, 1995). Finally, manufacturers increased their consumer and trade promotional expenses from 50% to 75% of marketing budgets during the 1985-90 time period (Forbes, 1991). Some researchers (e.g., Mela et al., 1997) warn us that reduced advertising increases consumers' price sensitivity. The possible reason for the trend could be that firms with high expectations are disappointed with the advertising effectiveness, and they tended to overspend on advertising (Aaker and Carman, 1982). For example, using field experiments, Lodish et al. (1995) found that half of the ads investigated did not work. While Tellis and Weiss (1995) found a small advertising effect on sales, others did not find any significant relationship between advertising and sales (e.g., Tellis, 1988a).

As a cointegration test examines the long term relationships among cointegrated variables, it does not entail causality. Instead, it indicates that the cointegrating variables tend to move in the long term in a pattern as revealed by the cointegrating vector. Although making causal inference is interesting and yet controversial, an effort is attempted.

The Granger causality tests indicate that both CON and DPI had a causal impact on AD, but AD did not cause either CON or DPI, which supports Berndt's (1991) conclusion. The classic finding by Schmalensee (1972) states that aggregate consumption has an impact on aggregate advertising, not vice versa. Thus, the accusation that advertising is responsible for spending is not supported at the macro level. However, marketers are not totally off the hook in that the GMD tests indicate a causal influence AD had on CON at the 10% level, which raises an interesting philosophical comment. That is, for a long lasting perception to endure among people it must be based on factual evidence of some sort.

6. MANAGERIAL AND RESEARCH IMPLICATIONS

Even though the study was carried out at the macro level, its findings have implications for managers and advertisers alike. As aforementioned, many early investigations on the advertising and sales relationship using annual Pinkham Medicine Company's historic data treated advertising as an exogenous variable (e.g., Palda, 1965; Clark, 1976; Weiss and Windal, 1980). On the same data, Baghestani (1991) found a bidirectional causation between the two variables with the aid of the cointegration technique. In other words, advertising does not have an exogenous property relative to sales. Other studies (e.g., Bass and Clarke, 1972) utilized different data for exploring advertising effects on sales. However, they suffered the same questionable assumption regarding the exogeneity of advertising.

This study at the macro level points out that while consumption had a causal impact on advertising in Granger sense, advertising had no causal influence on consumption. Although the GMD tests present weak evidence that advertising had a causal impact on consumption, taken all together, there certainly is not evidence in support of exogeneity of advertising. In fact, the issue is complicated because there are different degrees of exogeneity. Thus, we must keep causality and exogeneity separate (Maddala, 1992). As such, we must not automatically assume the exogeneity of advertising in studying the advertising-sales relationship. This finding also has value in guiding managers. For example, some managers believe that advertising is a cause for sales growth. Although it is weakly supported by the GMD test, this should not be taken for granted in light of other evidence.

As the cointegrating vector among AD, CON, and DPI exists, it demonstates that these three series have a long term equilibrium relationship, which can be interpreted in the following fashion. Over the long time horizon, when consumption increased by $1, firms on average would increase their advertising by $0.209, which could well reflect the market mechanism and/or company advertising policy that govern the sales and advertising relationship at the micro level. On the other hand, firms on average anticipated a $4.774 return for a $1 increase on advertising. The above relationship holds only in the long term. In the short run, firms may experience overadvertising or underadvertising, and excessive or mediocre returns from advertising. The market mechanism will correct these deviations in maintaining the long run equilibrium condition.

At the firm level, managers can use this information as the benchmark to evaluate their performance in terms of their advertising effectiveness. Aggregate data reflects the average value of good and bad performance. Also, managers should be aware that advertising and sales might be cointegrated. That is, there may exist a long term equilibrium relationship between them, which means that one may overspend on advertising in hopes of boosting short term sales, but its effect will be only temporary. Exceeding a certain point, the decreasing return on advertising might inevitably erode the profit margin.

7. CONCLUSION

In the marketing literature, the sales-advertising relationship has been a keen interest of inquiry for a long time. In the early days, distributed lag models were often used for exploring the topic. The major drawback of that approach lies in the troublesome assumption that advertising is an exogenous variable.

In this paper, we applied unit root and cointegration tests to the traditional marketing topic. We intentionally chose to explore the aggregate advertising and consumption using the U.S. data because macro models are vital in confirming micro models (Little, 1979). We purposely focused our analysis on the data from 1929 to 1997 because we wanted to ensure that our results were comparable to the previous studies. Also, the results from the chosen period help us explain some important trends. Our results show that during the period of 1929 to 1997 the mean advertising elasticity is 0.181, which is comparable to the finding by Assmus et al. (1984). Realizing price elasticity is eight times larger than the advertising elasticity (Tellis, 1988b), it is not surprising that more price cutting promotions are used in lieu of advertising in the past decade in spite of the warning that the practice increases consumers' price sensitivity (Mela et al., 1997).

According to Galbraith (1967), personal income leads to advertising, which in turn leads to consumption. However, Quarles and Jeffres (1983) suggested a different path in reporting that income influences consumption, which in turn impinges on advertising expenditures. We found that both disposable personal income and consumption have a causal impact on advertising in Granger sense, but advertising does not influence consumption in Granger sense, which is in line with the results conversed by Schmalensee (1972) and Ashley et al. (1977). Thus, it raises a serious doubt as to whether advertising has a causal impact on sales at the micro level, a relationship which many people believe in. At least, we should not take it for granted.

We found that advertising, disposable personal income, and consumption are cointegrated. That is, there is a long term equilibrium relationship among the three series. Advertising and disposable personal income tend to progress in the opposite directions, which lends an indirect support towards the discovery that advertising has a strong negative impact on the employment rate (Chowdhury, 1994). While this study may not lend a strong support to the charge that advertising is responsible for spending (Galbraith, 1967) based on the Granger tests, it invites some challenges marketers and advertisers have to face. The challenge that needs to be addressed is: what are the exact mechanisms through which advertising negatively affects personal income? Also, what can we do to remedy the problem and serve consumers' needs better? This is certainly worthy of further consideration.

TABLE 1

UNIT ROOT TESTS: 1929-1997

Variables         DF              ADF(1)            ADF(2)

AD                -1.266          -1.03(1)          -1.03
CON                0.098           0.972(8)         -0.111(1)
DPI               -0.67            1.223(10)        -0.633(1)
[DELTA]AD         -5.096 ***      -5.096 *** (0)    -5.096 *** (0)
[DELTA]CON        -3.617 ***      -0.374(6)         -0.374(6)
[DELTA]DPI        -4.498 ***      -0.439(10)        -2.26(4)

Notes: *** denotes p < 1%. AD, CON, and DPI are real data on aggregate
advertising, consumption, and disposable personal income for the U.S.
from 1929 to 1997. We use [DELTA] to represent the difference of the
series. If the numbers are less than the critical value at a given
significance level, meaning c in equation (1) and (2) is different from
zero, the nonstationarity of the series can be rejected. For the ADF
tests, two methods are used to determine the lag length, from
general-to-specific and from specific-to-general. While ADF(1) reports
the former, ADF(2) reports the latter results. For example, using the
general-to-specific method, we begin with the largest lag length, which
is 12 in our case, and we obtain our ADF statistics when the
coefficient for the largest lag (i.e., 12) is significant at the 10%
level. On the other hand, with the specific-to-general method, we begin
with lag length 1 and obtain our ADF statistics when the coefficient
for the shortest lag (i.e., 1) is significant at the 10% level. The
numbers in parentheses are the optimal lag length, which is the chosen
value for k in equation (2). For some variables, the number
chosen from the two methods is the same. With an intercept and time
trend, the critical values at the 1%, 5%, and 10% levels are -4.15,
-3.5, and -3.18, respectively. With an intercept and without a time
trend, the critical values at the 1%, 5%, and 10% levels are -3.58,
-2.93, and -2.60, respectively. These critical values, which are
derived from an observation size equal to 50, are from Fuller (1976,
p.373). It is concluded that all the three series are integrated of
order 1, I(1).

TABLE 2

JOHANSEN AND JUSELIUS'S TESTS FOR COINTEGRATION ANALYSIS (1929-1997)

Null hypothesis                Maximum eigenvalue test    Trace test

r = 0                                 22.49 **              32.75 **
r [less than or equal to] 1            6.05                 10.26
r [less than or equal to] 2            4.21 *                4.21 *

Test for Exclusion

AD     4.54 **       CON   10.67 **      DPI   11.31 **

Test for Stationarity

AD    11.33 **       CON   11.50 **      DPI   10.68 **

Note: ** denotes p < 5% and * denotes p < 10%. The null hypothesis of
no cointegrating vector is rejected by both the maximum eigenvalue and
trace tests. However, the null hypothesis of only one or less
cointegrating vector cannot be rejected by either test at the 5%
level. Thus, AD, CON, and DPI are cointegrated with only one
cointegrating vector. The chi-square exclusion test shows that the
null hypothesis of excluding any variable from the cointegrating
vector can be rejected at the 5% level. Also, the chi-square test for
stationarity indicates that the null hypothesis of stationarity can be
rejected for all the variables at the 5% level. The critical values
for cointegration tests are provided by Osterwald-Lenum (1992) and
Johansen and Juselius (1990).

TABLE 3

THE COINTEGRATING EQUATIONS

(1) -0.1062AD + 0.0223CON - 0.0177DPI
(1) AD = 0.209CON - 0.167DPI
(2) CON = 4.774AD + 0.797DPI
(3) DPI = -5.992AD + 1.255CON

Note: Equation (1) is the cointegrating vector for AD, CON, and DPI.
Equation (2), (3), and (4) are the normalized equations with respect to
AD, SER, and DPI, respectively, derived from equation (1). Thus,
equation (2), (3), and (4) reflect the same long term equilibrium
relationship among the three variables as equation (1) does, but from a
different angle. These equations describe a stable condition of
equilibrium over the period of from 1929 to 1997. For instance, for a
$1 increase in AD, DPI tended to drop $5.992 to maintain the
equilibrium relationship between them. However, this interpretation
does not implicate any causal linkage among the variables.

TABLE 4

THE COINTEGRATiNG EQUATIONS

(1) 5.3076lnAD - 29.3681lnCON + 23.4919lnDPI
(2) lnAD = 5.533lnCON - 4.426lnDPI
(3) lnCON = 0.181lnAD + 0.800lnDPI
(4) lnDPI = -0.226lnAD + 1.250lnCON

Note: Equation (1) is the cointegrating vector for InAD, InCON, and
InDPI. Equation (2), (3), and (4) are the normalized equations with
respect to InAD, InCON, and InDPI, respectively, derived from equation
(1). Thus, equation (2), (3), and (4) reflect the same long term
equilibrium relationship among the three variables as equation (1)
does, but from a different angle. These equations describe a stable
condition of equilibrium over the period of from 1929 to 1997. Since
the logged values are used, the parameters represent elasticity. For
instance, for one percent increase in AD, CON tended to increase 0.181
percent. Thus, the long terms advertising elasticity is 0.181, which is
slightly lower than 0.22, the mean elasticity of advertising from a
meta-analysis (Assmus et al. 1984).

TABLE 5

GRANGER CAUSALITY TESTS

(1) A[D.sub.t] = u + [[summation].sub.i][[PI].sub.i]A[D.sub.t-i] +
  [[summation].sub.i][[PI].sub.i] CO[N.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
(2) A[D.sub.t] = u + [[summation].sub.i][[PI].sub.i]A[D.sub.t-i] +
  [[summation].sub.i][[PI].sub.i] DP[I.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
(3) CO[N.sub.t] = u + [[SIGMA].sub.i][[PI].sub.i] CO[N.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]A[D.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
(4) CO[N.sub.t] = u + [[summation].sub.i][[PI].sub.i]CO[N.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]DP[I.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
(5) DP[I.sub.t] = u + [[summation].sub.i][[PI].sub.i]DP[I.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]CO[N.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
(6) DP[I.sub.t] = u + [[summation].sub.i][[PI].sub.i]DP[I.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]A[D.sub.t-1] + [[epsilon].sub.t],
  where i goes from 1 to p.
F-statistics for testing Ho: [[summation].sub.i][[PI].sub.i] = 0.

With p =4, for equation (1) and (2), F values for excluding CON and
  DPI, respectively,

CON    5.76543    DPI    2.68956 **

With p = 4, for equation (3) and (4), F values for excluding AD and
  DPI, respectively,

AD     0.3253     DPI    0.55879

With p = 4, for equation (5) and (6), F values for excluding CON and
AD, respectively,

CON    2.57897    AD    1.04113

Note: * denotes p < 10%, ** denotes p < 5%, and *** denotes p < 1%. The
Granger test examines whether the joint coefficients for a given
variable other than the lagged dependent variable in the equation are
equal to zero. For instance, for equation (1), we test whether the
joint coefficients for CON are equal to zero. The test used is F
statistics. The essence of the Granger test is to see whether the
lagged values of a given variable would help explain the dependent
variable when the lagged values of the dependent variable are present.
The results indicate CON and DPI have a Granger causal impact on AD,
not vice versa.

TABLE 6

GEWEKE-MEESE-DENT CAUSALITY TESTS

(1) A[D.sub.t] = u + [[summation].sub.i][[PI].sub.i]A[D.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]CO[N.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]CO[N.sub.t+i] + CO[N.sub.t] + [[epsilon].sub.t], where i
  goes from 1 to p.
(2) A[D.sub.t] = u + [[summation].sub.i][[PI].sub.i]A[D.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]DP[I.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]DP[I.sub.t+i] + DP[I.sub.t+i] + [[epsilon].sub.t], where
  i goes from 1 to p.
(3) CO[N.sub.t] = u + [[summation].sub.i][[PI].sub.i]CO[N.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]A[D.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]A[D.sub.t+i] + A[D.sub.t] + [[epsilon].sub.t], where i
  goes from 1 to p.
(4) CO[N.sub.t] = u + [[summation].sub.i][[PI].sub.i]CO[N.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]DP[I.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]DP[I.sub.t+i] + DP[I.sub.t] + [[epsilon].sub.t], where i
  goes from 1 to p.
(5) DP[I.sub.t] = u + [[summation].sub.i][[PI].sub.i]DP[I.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]CO[N.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]CO[N.sub.t+i] + CO[N.sub.t] + [[epsilon].sub.t], where i
  goes from 1 to p.
(6) DP[I.sub.t] = u + [[summation].sub.i][[PI].sub.i]DP[I.sub.t-i] +
  [[summation].sub.i][[PI].sub.i]A[D.sub.t-1] + [[summation].sub.i]
  [[PI].sub.i]A[D.sub.t+i] + A[D.sub.t] + [[epsilon].sub.t], where i
  goes from 1 to p.
F-statistics for testing Ho: [[summation].sub.i][[PI].sub.i] = 0.

With p=4, for equation (1) and (2), F values for excluding
  [[summation].sub.i][[PI].sub.i]CO[N.sub.t+i] and [[summation].sub.i]
  [[PI].sub.i]DP[I.sub.t+i], respectively,

CON    0.42184    DPI    1.16925

With p = 4, for equation (3) and (4), F values for excluding
  [[summation].sub.i][[PI].sub.i]A[D.sub.t+i] and [[summation].sub.i]
  [[PI].sub.i]DP[I.sub.t-i], respectively,

AD     2.52741    DPI    1.40945

With p = 4, for equation (5) and (6), F values for excluding
  [[summation].sub.i][[PI].sub.i]CO[N.sub.t+i] and [[summation].sub.i]
  [[PI].sub.i]A[D.sub.t+i] respectively,

CON 0.69152       AD     0.60671

Note: denotes p < 10%, denotes p < 5%, and denotes p < 1%. The
Geweke-Meese-Dent test examines whether the joint coefficients of
future values for a given variable other than the dependent variable in
the equation are equal to zero. For example, in equation (1), with AD
as the dependent variable, the independent variables include lagged AD
(lags 1 to 4), lagged CON (lags 1 to 4), current CON, and future CON
(in future periods 1 to 4). The null hypothesis is that the joint
coefficients of future CON (next four periods) is zero. That is, the
future values of CON do not affect current AD. The results are
different from those of the Granger tests. The only significant
relationship is that AD had a causal impact on CON at the 10% level.

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Dr. Chiquan Guo earned his Ph.D. at Southern Illinois University at Carbondale in 2002. Currently he is an assistant professor of marketing and international business at the University of Texas-Pan American.