a cointegration analysis of advertising and sales data

Review of Industrial Organization18: 417–426, 2001.© 2001Kluwer Academic Publishers. Printed in the Netherlands.

417

A Cointegration Analysis of Advertising and SalesData

CAROLINE ELLIOTT?Department of Economics, The Management School, Lancaster University, Lancaster LA1 4YX,U.K.

Abstract. It is argued that the nature of the industry level relationship between advertising andsales can give some indication of the form of competition in an industry. Hence, this paper examineswhether there is a long-run, stable, equilibrium relationship between advertising and sales for foodand soft drinks industries. Results suggest that the variables are non-stationary, but do not containseasonal unit roots. Cointegration is not identified between soft drinks industry advertising and sales,which, together with the results of differenced variable regressions, suggests that rivalry betweenfirms in this industry may be intense.

Key words: Advertising, cointegration, sales, unit roots.

JEL Classifications:C2, C5, L1.

I. Introduction

The nature of the industry level relationship between advertising and sales cangive some indication of the form of competition in an industry. If industry de-mand has not yet reached saturation point, a positive, stable, long-run relationshipbetween advertising and sales may reflect firms’ use of advertising primarily toattract new consumers and to increase purchases by existing consumers. Alternat-ively, in mature, saturated industries, advertising may be used to maintain customerloyalty and/or redistribute market shares. Rivalry between firms may be intense andcointegration between advertising and sales will be less likely. Hence, this paperexamines whether advertising and sales in the U.K. food industry and the moreclosely defined soft drinks industry are cointegrated, in order to help determine thenature of competition in these industries.

In existing research, Baghestani (1991) and Zanias (1994) used the U.S. LydiaPinkham Company data to confirm that a long-run equilibrium, cointegrating, re-lationship existed between advertising expenditure and sales. The results of errorcorrection mechanism (ECM) modelling indicated that movements in advertising? I would like to thank Lisa Hart, Geraint Johnes, Denise Osborn, David Sapsford, Mohammed

Salisu, David Young, the editor and two referees for helpful comments at various stages of the writingof this paper. The usual disclaimer, of course, applies.

418 CAROLINE ELLIOTT

expenditure ensured that convergence to the long-run equilibrium position wasachieved. However, the Lydia Pinkham company produced only one product, “a ve-getable remedy for menstrual problems” (Baghestani, 1991, p. 672). Therefore, fur-ther empirical analyses are still required to confirm whether long-run cointegratingrelationships between firm level advertising and sales exist more generally.

Yet, the results of such firm-level analyses cannot be used to determine thenature of competition in an industry. Even if firm level advertising and sales arecointegrated, this does not necessarily imply that industry level advertising andsales will be similarly related. It is conceivable that relatively strong cointegratingrelationships may be found between advertising expenditure and sales variables at afirm or brand level, when, as was true of the Lydia Pinkham product, the good waslargely promoted by advertising alone. However, such relationships may be lesslikely to occur at an industry level.1 Factors other than advertising affect sales, andadvertising may only be one of a number of strategies employed to influence sales.Further, as argued above, a cointegrating relationship between these industry levelvariables may only be expected under certain circumstances. Nevertheless, it isimportant for firms to understand the nature of any long-run stable relationship thatmay exist between advertising and sales as this can impact upon their marketingdecisions. In addition, if progress can be made in understanding the relationshipbetween advertising and sales, further understanding of the relationships betweenadvertising and variables such as price, profits and market structure may then alsobe achieved.

There is also a growing body of research that examines whether aggregateadvertising and consumption (sales) are cointegrated, see for example, Jung andSeldon (1995), Seldon and Jung (1995). Such macro level analyses can contrib-ute to debate as to the nature of relationships between advertising, consumption,aggregate demand, saving and investment. However, the results of studies into thenature of the relationship between industry level advertising and sales cannot begeneralised to a macro level, given the diverse nature and experiences of the manyindustries within a country.

The food industry and the more specific soft drinks industry were chosen partlybecause advertising is relatively important in both. Percentage advertising-salesratios were calculated for both industries for 1991, and were identified as relativelyhigh.2 For the food industry the advertising-sales ratio was 1.78%, and for the softdrinks industry 0.82%, although this was lowered by a low advertising-sales ratiofor fruit juice and fruit drinks.3

1 Nevertheless, Dekimpe and Hanssens (1995) suggest that industry level sales variables are morelikely to be non-stationary than comparable firm level data.

2 Using data from the Advertising Statistics Yearbook 1993, the final year in which required datawere available in this publication.

3 Using data from the same source, the advertising-sales ratio for the clothing and footwearindustry was 0.16%, and was 0.85% for alcoholic drinks.

A COINTEGRATION ANALYSIS OF ADVERTISING AND SALES DATA 419

Also, to aid comparisons that may be made with cointegration studies of theLydia Pinkham data, non-durable consumer products that contain experience aswell as search characteristics were required, as the Lydia Pinkham product couldbe similarly described. Analysis is restricted to searching for cointegration in abivariate regression context. This also aids comparability with the analyses ofBaghestani (1991) and Zanias (1994) that restrict attention to a bivariate modelformulation.

II. Data

Quarterly data were collected for advertising and sales in the food and the softdrinks industries. The use of quarterly data is warranted as attempts can then bemade to identify any shorter-run advertising effects on sales that may be less ap-parent in annual data. It also seems plausible that the impact of advertising on salesin the food and soft drinks industries, and more generally in consumer non-durableindustries, including the industry analysed by Baghestani, will occur within monthsrather than within the longer time span of a year (Clarke, 1976; Zanias, 1994). If, inthese circumstances annual data is used, it has been argued that estimation resultsare likely to be affected by data interval bias, whereby the impact of advertisingon sales will be exaggerated.4 Further, it seems reasonable to suppose that indi-viduals may forget many of the advertising messages they receive (particularly fornon-durable products) within a year, so annual data may be inappropriate.5

However, it is the time span of the data rather than the number of observationsthat is of primary relevance for statistical analysis of long-run relationships. Con-sequently, the current analysis can only provide information on long-run industrylevel relationships between advertising and sales over a maximum of eleven years.Further, whilst it is undoubtedly preferable to use quarterly as opposed to annualdata to avoid data interval bias, it may be argued that weekly or monthly data areeven more appropriate, as this would more accurately reflect the interval betweenpurchases.

The data series were plotted to see if any general properties of the data couldbe identified. Plots suggested (unsurprisingly) that most of the variables are sea-sonal in nature – particularly the soft drinks variables and the food advertisingvariable.6 Note that the seasonal nature of the data must then be taken into account,a consideration not required of the Lydia Pinkham annual data.7

4 There is a very extensive literature on this issue, see for example, Clarke (1976) and Bass andLeone (1983).

5 Whilst some advertising campaigns are very memorable, it is hypothesised that the vast majorityof advertisements encountered are forgotten within the period of a year.

6 Details available from author on request.7 Seasonally adjusted data were not employed, as it is believed that in seasonally adjusting data,

information on the dynamic behaviour of variables is often lost, particularly in smaller data sets.


Table I. Spurious regression test results

xi LFEXCa LFAECb LSDSCc LSDAECd

CONST 8.2360∗∗∗,e −29.8238∗∗∗ 4.0091∗∗∗ −1.7609

SEAS1 −0.0757∗∗∗ 0.2284∗∗∗ −0.0858 −0.4208∗∗SEAS2 −0.0121 −0.0058 −0.0994 0.7199∗∗∗SEAS3 −0.0041 −0.0455 −0.0138 0.5659∗∗∗LFAEC 0.1754∗∗∗LFEXC 3.8109∗∗∗LSDAEC 0.2164∗∗∗LSDSC 1.7667∗∗∗R̄2 0.8832 0.7329 0.6771 0.8055

DW 1.5046 1.4989 1.0862 1.7755

LMf (p-value) 0.652 0.711 0.001 0.009

RESET (p-value) 0.176 0.051 0.109 0.000

a LFEXC = logged food expenditure in constant prices.b LFAEC = logged food advertising expenditure in constant prices.c LSDSC = logged soft drinks sales in constant prices.d LSDAEC = logged soft drinks advertising expenditure in constant prices.e∗∗,∗∗∗ Denote significance at the 5% and 1% levels, respectively, in a standardt-test.f The LM test is ax2 test for the presence of fourth-order autocorrelation.

III. Results

1. PRELIMINARY ANALYSIS8

Initially, a test for the presence of spurious regression problems was performed. Ifa basic OLS regression

yi = a + bxi + ei (1)

results in theR2 being greater than the Durbin–Watson (DW) statistic, this is a rule-of-thumb indication that a spurious regression problem has been modelled (Gujar-ati, 1995). Nevertheless, it should be noted that if the variables are subsequentlyfound to beI (1), then the OLS results should be treated carefully. The OLS regres-sions will be the long-run regressions if cointegrating relationships between twovariables are subsequently identified, but the t test statistics will be non-standard.Because of the seasonal nature of the quarterly data employed, regressions withseasonal dummies included are reported.

No evidence of a spurious regression problem was found between the variablepairings.

8 Generally, details of the methodology adopted are not included as many of the tests and methodsreported can be found in texts such as Harris (1995).


Whilst the estimated OLS regressions reported in Table I were generally robustas to whether the data were logged or not, logged data are used throughout the ana-lysis below.9,10 The results of testing each variable for the presence of conventionalunit roots were also robust to whether the data were logged or not.

2. UNIT ROOT TESTING

The Osborn, Chui, Smith and Birchenhall 1988 (OCSB) test checks for the pres-ence of both conventional and seasonal unit roots.11 A regression of

(1− L)(1− L4)Xt = α1Q1,t + α2Q2,t + α3Q3,t + α4Q4,t

+β1(1− L4)Xt−1+ β2(1− L)Xt−4

+p∑i=1

φi(1− L)(1− L4)Xt−i + εt , (2)

whereQ = quarter; results in a null hypothesis ofH0 : Xt ∼ I (1,1) being testedagainst two possible alternative hypothesesH1 : Xt ∼ I (1,0) andH2 : Xt ∼I (0,1). H0 is rejected in favour ofH1 if β1 = 0 andβ2 < 0, whilstH0 is rejectedin favour ofH2 if β1 < 0, andβ2 = 0. The null hypothesis is not rejected if wecannot rejectH0 : β1 = β2 = 0. If seasonal unit roots are not found to be present,the seasonality may be assumed to be a result of stationary seasonal processes, andfurther modelling should include seasonal dummy variables.

For each data series examined, four lags were employed in the test, as uni-variate regressions had indicated that all of the variables were characterised byfourth-order autocorrelation.12 Results reported in Table II consistently indicatedthat we could reject the null hypothesis of both conventional and seasonal unitroots for each of the data series. The alternative hypothesisH2, non-rejection ofwhich indicates the presence of seasonal but not conventional unit roots, was alsorejected easily for each variable. However, the alternative hypothesisH1 could notbe rejected for any variable, and only failed to be rejected at the 1% significancelevel for LSDAEC.

The results of the OCSB test have confirmed the absence of seasonal unit rootsin the data series. However, because the hypothesis ofI (0,0) is not directly tested,for thoroughness, augmented Dickey–Fuller tests were performed to confirm thatthe data series areI (1,0) as opposed toI (0,0). Results are reported in Table III.

9 It was expected that the data would be robust to being logged or not, as inspection of the dataplots (see author for details) suggests that the overall levels of the data change very little over time.

10 The R̄2s are a little higher in the logged data regressions, whilst the Durbin-Watson statisticswere very similar in the linear and double-log models. Further, the RESET test statistics, whichindicate suitable functional form, were satisfactory when logged data were adopted. The non-loggedresults remain available from the author.

11 However, the test cannot identify every possible seasonal unit root.12 Results available from author on request.


Table II. OCSB test results

NULL: I (1, 1) variable β1 = 0b,c β2 = 0 β1 = β2 = 0d

LFAEC −1.0492 −4.0774∗∗∗,a 14.2558∗∗∗LFEXC −1.4090 −3.0712∗∗∗ 8.8594∗∗∗LSDAEC −1.7077 −2.1423∗∗ 4.4567∗∗LSDSC −1.1193 −3.9672∗∗∗ −11.1736∗∗∗

a∗∗,∗∗∗ Denotes significance at the 5% and 1% levels respectively.b β1, β2 are defined as in Equation (2).c Columns 2 and 3 representt-test results.d Column 4 representsF -test results.

Table III. ADF test results

NULL: I (1) variable ADF test value Critical valuesa

LFAEC −1.4177 −2.9358LFEXC −2.1852 −2.9358LSDAEC −1.1089 −2.9287LSDSC −0.5352 −2.9287

a The critical values are MacKinnon 95% critical values.

Again, four lags were included in each test, and the results reported are fromtests without time trends, although results were robust to their inclusion.13 The nullhypothesis of a unit root could not be rejected for any variable.

3. TESTING FORCOINTEGRATION

Due to the non-stationary nature of the variables, it was necessary to investigatewhether advertising and sales are cointegrated in the U.K. food and soft drinks in-dustries, although the absence of seasonal unit roots implied that seasonal cointeg-ration techniques were not required. The OLS regressions reported in Table I can beused to test for cointegration and will be the long-run, cointegrating relationshipsif advertising and sales are believed to be cointegrated.

No formal test was required to confirm that advertising and sales are cointeg-rated in the U.K. food industry data set: these variables must be cointegrated if theyare bothI (1,0), whilst the residuals of the OLS regressions (see Table I) are notserially correlated.14 This suggests that there is a stable, long-run, equilibrium rela-

13 It is recognised that the small sample properties of the (Augmented) Dickey–Fuller tests arerelatively weak. However, the result that each variable has a conventional unit root was confirmed byperforming the Bayesian odds ratio test (Sims, 1988).

14 The DW tests are inconclusive, although the test statistics are very close to the upper bound at the1% significance level. Hence, Lagrange multiplier tests for the presence of first-order autocorrelationwere carried it. The results suggested that the null hypothesis of no autocorrelation could not berejected at any reasonable significance level.


Table IV. ADF test results II

yi xi ADF test value Critical valuea

LSDSC LSDAEC −0.9875 −4.7822LSDAEC LSDSC −1.8795 −4.7822

a The critical value is a MacKinnon 95% critical value.

tionship between food advertising and sales, and, for example, that any variation insales, as a result of changes in advertising expenditures, take place within the samethree month period as the change in industry level advertising.15 Consequently,distinct cointegration and ECM models are not required to model the long-run andshort-run relationships between food industry advertising and sales.

As a formal test for cointegration between soft drinks advertising and sales,fourth-order ADF tests on the residuals of the long-run OLS regressions, includingseasonal dummies but not time trends, were performed (see Table IV).

In both regressions the null hypothesis of a unit root was clearly not rejected forthe residuals at the 5% significance level. Hence, whilst each variable was foundto be non-stationary, there is evidence to suggest that the residuals of the OLSregressions are similarly non-stationary. This implies that advertising and sales arenot cointegrated. Further tests for cointegration were not performed as Engle andGranger (1987) argue in favour of the use of the ADF test in this bivariate context,rather than, for example, VAR tests, due to its general robustness.16

4. DIFFERENCEDVARIABLE REGRESSIONS

Whilst advertising and sales have been found to be cointegrated in the food in-dustry, ECMs are not required to model, for example, the short-run adjustment ofadvertising to ensure that sales converge to their equilibrium level. This is becauseit has been concluded that all adjustment takes place within a single quarter.

Cointegration between soft drinks advertising and sales has not been found,although these variables are non-stationary. Hence, it is inappropriate to modelthe relationship between these variables using variables in levels. The statisticalrelationship between these variables should be modelled using variables in dif-ferences. Results of this modelling are reported in Table V. The first and thirdregressions reported are the most general regressions estimated, whilst the secondand final regressions are the preferred regressions, obtained after insignificant (atthe 10% significance level or above), differenced, lagged variables were deleted.When differenced sales is the dependent variable, the coefficients on the seasonaldummy variables and DLSDSC1 have the expected signs. The coefficients asso-ciated with the variable DLSDAEC were insignificant, but this may reflect firms’

15 This seems plausible.16 Baghestani (1991) also only applies the ADF test as a test for cointegration.


Table V. Differenced variable regressions

xi DLSDSC DLSDSC DLSDAEC DLSDAEC

CONST −0.1656∗,a −0.1515∗∗∗ −0.3729 −0.3999SEAS1b −0.2743∗∗ −0.2536∗∗∗ −0.2101 −0.2692SEAS2 0.4042∗∗ 0.4166∗∗∗ 1.2764 1.3518∗∗SEAS3 0.5544∗∗∗ 0.4708∗∗∗ 0.5134 0.6162DLSDSCc 0.2982DLSDSC1d −0.6541∗∗∗ −0.6221∗∗∗ 0.2605DLSDSC2e −0.0550 1.1959 1.0696∗DLSDSC3 0.1433 0.1017DLSDAEC 0.0134 −0.0322DLSDAEC1 0.0219 −0.4980∗∗∗ −0.4895∗∗∗DLSDAEC2 0.0760∗ −0.6946∗∗∗ −0.6816∗∗∗DLSDAEC3 0.0228 −0.3986∗∗ −0.3906∗∗∗R̄2 0.9154 0.9151 0.9042 0.91165DW 1.9170 1.9363 2.2553 2.2474LM (p-value) 0.671 1.000 0.232 0.307RESET (p-value) 0.387 0.642 0.026 0.023

a∗,∗∗,∗∗∗ Denotes significance at the 10%, 5% and 1% levels respectively.b SEASi = seasonal dummy, wherei = 1, 2, 3, 4.c D(variable name) = differenced variable.d (variable name) 1 = variable lagged one period.e (variable name) 2 = variable lagged two periods, etc.

use of advertising to increase own sales at the expense of that of rivals, such thatindustry sales are insignificantly affected by changes in advertising expenditure.17

The results are not as satisfactory when DLSDAEC is the dependent variable, asevidenced by the results of the RESET test.

Whilst advertising and sales for the soft drinks industry were not found to becointegrated, tests for cointegration are not reliable when relatively short data seriesare employed. Therefore, it remains possible that soft drinks advertising and salesare cointegrated. To allow for this possibility, ECMs of the potential short-runrelationships between the variables were developed and the results are availableon request. However, the results obtained do not differ appreciably from thoseobtained from the differenced variable regressions, set out in Table V above, bothin terms of the signs of estimated coefficient values and diagnostic test results.

IV. Conclusions

The results of testing for cointegration verify whether there is a long-run, stablerelationship between economic variables. Cointegration between advertising andsales for food industry, but not soft drinks industry, data has been identified. Results

17 The coefficients on lagged DLSDAEC variables were also, typically, found to be insignificant.


suggest that advertising has a significant, positive effect on food industry sales,and that this relationship appears to be a stable, cointegrating one (even though,undoubtedly, some food advertising expenditures serve to counteract the effects ofrivals’ advertising within this broad industry category). The findings are importantas it was suggested in the introduction that industry level advertising and sales aremore likely to be cointegrated in industries where saturation levels of demand havenot yet been attained. A long-run, stable relationship between industry advertisingand sales is much less likely if rivalry between firms in an industry is intense, and ifthe saturation level of demand has been reached. In the more narrowly defined softdrinks industry, cointegration between advertising and sales has not been identified,as may be expected if a greater proportion of advertising serves to redistributeexisting market shares, and/or if advertising expenditures simply counteract theintended effects of rivals’ advertising. Evidence supporting such a use of advert-ising was found in Section III.4. This description seems appropriate for the softdrinks industry, when one considers the competition between well-known brandssuch as Coca-Cola and Pepsi. Hence, the results suggest that in very competitive,oligopolistic markets, cointegrating relationships between industry advertising andsales may be less likely.

Yet, our conclusions are made only tentatively. Both tests for unit roots andcointegration are relatively unreliable when comparatively small data sets are used.However, the data for both industries represent the longest consistent time-spansof quarterly data available. Further, a bivariate analysis was employed to maintaincomparability with the firm level analyses of Baghestani (1991) and Zanias (1994).However, an obvious potential direction for future research is the expansion ofthe present analysis to a multivariate context. It is possible that when multivariateJohansen cointegration testing methods are employed, industry level advertisingand sales may be confirmed to be cointegrated. Muscatelli and Hurn (1992) suggestthat omitted variables will tend to obscure cointegrating relationships.

The use of seasonally unadjusted quarterly data necessitated the use of the morecomplex tests required to test for seasonal unit roots. Such tests remain uncommonin industrial economics applications, but may increasingly be used in the future.Existing research on data interval bias suggests that it may often be inappropriateto use annual data when trying to estimate the relationship between advertising andsales. Nevertheless, only conventional unit roots were found to occur, so a standardcointegration test rather than seasonal cointegration techniques could be applied.

Data Appendix

Quarterly data on food advertising expenditure were obtained from theAdvert-ising Statistics Yearbook(published by the Advertising Association) for the period1983(1) to 1992(4). Quarterly data on consumers’ expenditure on food were takenfrom theMonthly Digest of Statistics. Consumers’ food expenditure is employed asa measure of sales, as the chief difference between sales and expenditure should be


the source of the data, i.e., sales data are collected from firms, whilst expenditureinformation is collected from households.

Soft drinks advertising expenditures were obtained from MEAL data (MediaExpenditure Analysis Limited). As a measure of industry sales, quarterly dataon the total sales of principal products were obtained from the Business MonitorPQ4283 for the period 1982(1) to 1992(4).18

The values of each variable are in constant prices (1987 = 100), calculated usingthe average annual Retail Prices Index for all items. This is the method adoptedin the Advertising Statistics Yearbook. It should also be noted that no obviousalternative price deflator was available as a consistent data series over the periodcovered by the data set.

References

Baghestani, H. (1991) ‘Cointegration Analysis of the Advertising-Sales Relationship’,Journal ofIndustrial Economics, 39, 671–681.

Bass, F. M., and R. P. Leone (1983) ‘Temporal Aggregation, the Data Interval Bias, and EmpiricalEstimation of Bimonthly Relations from Annual Data’,Management Science, 29, 1–11.

Clarke, D. G. (1976) ‘Econometric Measurement of the Duration of Advertising Effect on Sales’,Journal of Marketing Research, 13, 345–357.

Dekimpe, M. G., and D. M. Hanssens (1995) ‘Empirical Generalizations about Market Evolutionand Stationarity’,Marketing Science, 14, G109–G121.

Engle, R. F., and C. W. J. Granger (1987) ‘Cointegration and Error Correction: Representation,Estimation, and Testing’,Econometrica, 55, 251–276.

Gujarati, D. N. (1995)Basic Econometrics, 3rd edn. New York: McGraw Hill, Inc.Harris, R. (1995)Using Cointegration Analysis in Econometric Modelling. Hemel Hempstead:

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Economic Surveys, 6, 1–43.Osborn, D. R., A. P. L. Chui, J. P. Smith, and C. R. Birchenhall (1988) ‘Seasonality and the order of

Integration for Consumption’,Oxford Bulletin of Economics and Statistics, 50, 361–377.Seldon, B. J., and C. Jung (1995) ‘The Length of the Effect of Aggregate Advertising on Aggregate

Consumption’,Economics Letters, 48, 207–211.Sims, C. A. (1988) ‘Bayesian Skepticism on Unit Root Econometrics’,Journal of Economic

Dynamics and Control, 12, 463–474.Zanias, G. P. (1994) ‘The Long-Run, Causality, and Forecasting in the Advertising-Sales Relation-

ship’, Journal of Forecasting, 13, 601–610.

18 Note that it was possible to use four additional observations at the beginning of the data set thanwere available for the food industry data.

a cointegration analysis of advertising and sales data

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