Mix (1)

506

24MODELING MARKETING MIX

GERARD J. TELLIS

University of Southern California

CONCEPT OF THE MARKETING MIX

The marketing mix refers to variables that amarketing manager can control to influencea brand’s sales or market share. Traditionally,these variables are summarized as the four Ps ofmarketing: product, price, promotion, and place(i.e., distribution; McCarthy, 1996). Productrefers to aspects such as the firm’s portfolio ofproducts, the newness of those products, theirdifferentiation from competitors, or their super-iority to rivals’ products in terms of quality.Promotion refers to advertising, detailing, orinformative sales promotions such as featuresand displays. Price refers to the product’s listprice or any incentive sales promotion such asquantity discounts, temporary price cuts, ordeals. Place refers to delivery of the productmeasured by variables such as distribution,availability, and shelf space.

The perennial question that managers face is,what level or combination of these variablesmaximizes sales, market share, or profit? Theanswer to this question, in turn, depends on thefollowing question: How do sales or marketshare respond to past levels of or expenditureson these variables?

PHILOSOPHY OF MODELING

Over the past 45 years, researchers have focusedintently on trying to find answers to this ques-tion (e.g., see Tellis, 1988b). To do so, they havedeveloped a variety of econometric models ofmarket response to the marketing mix. Most ofthese models have focused on market responseto advertising and pricing (Sethuraman & Tellis,1991). The reason may be that expenditureson these variables seem the most discretionary,so marketing managers are most concernedabout how they manage these variables. Thischapter reviews this body of literature. Itfocuses on modeling response to these vari-ables, though most of the principles apply aswell to other variables in the marketing mix. Itrelies on elementary models that Chapters 12and 13 introduce. To tackle complex problems,this chapter refers to advanced models, whichChapters 14, 19, and 20 introduce.

The basic philosophy underlying the approachof response modeling is that past data on con-sumer and market response to the marketingmix contain valuable information that canenlighten our understanding of response. Thosedata also enable us to predict how consumers

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might respond in the future and therefore howbest to plan marketing variables (e.g., Tellis &Zufryden, 1995). While no one can assert thefuture for sure, no one should ignore the pastentirely. Thus, we want to capture as much infor-mation as we can from the past to make validinferences and develop good strategies for thefuture.

Assume that we fit a regression model inwhich the dependent variable is a brand’s salesand the independent variable is advertising orprice. Thus,

Yt = α + βAt + εt.

Here, Y represents the dependent variable(e.g., sales), A represents advertising, the para-meters α and β are coefficients or parametersthat the researcher wants to estimate, and thesubscript t represents various time periods.A section below discusses the problem ofthe appropriate time interval, but for now, theresearcher may think of time as measured inweeks or days. The εt are errors in the estima-tion of Yi that we assume to independently andidentically follow a normal distribution (IIDnormal). Equation (1) can be estimated byregression (see Chapter 13). Then the coef-ficient β of the model captures the effect ofadvertising on sales. In effect, this coefficientnicely summarizes much that we can learn fromthe past. It provides a foundation to designstrategies for the future. Clearly, the validity,relevance, and usefulness of the parametersdepend on how well the models capture pastreality. Chapters 13, 14, and 19 describe howto correctly specify those models. This chapterexplains how we can implement them inthe context of the marketing mix. We focus onadvertising and price for three reasons. First,these are the variables most often under thecontrol of managers. Second, the literature hasa rich history of models that capture responseto these variables. Third, response to thesevariables has a wealth of interesting patterns oreffects. Understanding how to model theseresponse patterns can enlighten the modeling ofother marketing variables.

The first step is to understand the varietyof patterns by which contemporary markets

respond to advertising and pricing. These patternsof response are also called the effects of adver-tising or pricing. We then present the mostimportant econometric models and discuss howthese classic models capture or fail to captureeach of these effects.

PATTERNS OF ADVERTISING RESPONSE

We can identify seven important patterns ofresponse to advertising. These are the current,shape, competitive, carryover, dynamic, content,and media effects. The first four of these effectsare common across price and other marketingvariables. The last three are unique to advertising.The next seven subsections describe these effects.

Current Effect

The current effect of advertising is thechange in sales caused by an exposure (or pulseor burst) of advertising occurring at the sametime period as the exposure. Consider Figure 24.1.It plots time on the x-axis, sales on the y-axis,and the normal or baseline sales as the dashedline. Then the current effect of advertising is thespike in sales from the baseline given an expo-sure of advertising (see Figure 24.1A). Decadesof research indicate that this effect of advertis-ing is small relative to that of other marketingvariables and quite fragile. For example, thecurrent effect of price is 20 times larger thanthe effect of advertising (Sethuraman & Tellis,1991; Tellis, 1989). Also, the effect of advertis-ing is so small as to be easily drowned out by thenoise in the data. Thus, one of the most impor-tant tasks of the researcher is to specify themodel very carefully to avoid exaggerating orfailing to observe an effect that is known to befragile (e.g., Tellis & Weiss, 1995).

Carryover Effect

The carryover effect of advertising is thatportion of its effect that occurs in time periodsfollowing the pulse of advertising. Figure 24.1shows long (1B) and short (1C) carryover effects.The carryover effect may occur for several rea-sons, such as delayed exposure to the ad, delayed

Modeling Marketing Mix–•–507

(1)


A: Current Effect

Sales

Time Time

B: Carryover Effects ofLong-Duration

Sales

C: Carryover Effectsof Short-Duration

Time

Sales

D: Persistent Effect

34

Sales

Time

= ad exposureLegend: = baseline sales = sales due to ad exposure

Figure 24.1 Temporal Effects of Advertising

consumer response, delayed purchase due toconsumers’ backup inventory, delayed purchasedue to shortage of retail inventory, and purchasesfrom consumers who have heard from those whofirst saw the ad (word of mouth). The carryovereffect may be as large as or larger than the cur-rent effect. Typically, the carryover effect is ofshort duration, as shown in Figure 24.1C, ratherthan of long duration, as shown in Figure 24.1B

(Tellis, 2004). The long duration that researchersoften find is due to the use of data with longintervals that are temporally aggregate (Clarke,1976). For this reason, researchers should usedata that are as temporally disaggregate as theycan find (Tellis & Franses, in press). The totaleffect of advertising from an exposure of adver-tising is the sum of the current effect and all ofthe carryover effect due to it.

508–•–CONCEPTUAL APPLICATIONS



Shape Effect

The shape of the effect refers to the changein sales in response to increasing intensity ofadvertising in the same time period. The inten-sity of advertising could be in the form of expo-sures per unit time and is also called frequencyor weight. Figure 24.2 describes varying shapesof advertising response. Note, first, that thex-axis now is the intensity of advertising (in aperiod), while the y-axis is the response of sales(during the same period). With reference toFigure 24.1, Figure 24.2 charts the height of thebar in Figure 24.1A, as we increase the expo-sures of advertising.

Figure 24.2 shows three typical shapes: lin-ear, concave (increasing at a decreasing rate),and S-shape. Of these three shapes, the S-shapeseems the most plausible. The linear shape isimplausible because it implies that sales willincrease indefinitely up to infinity as advertisingincreases. The concave shape addresses theimplausibility of the linear shape. However, theS-shape seems the most plausible because itsuggests that at some very low level, advertisingmight not be effective at all because it getsdrowned out in the noise. At some very high

level, it might not increase sales because themarket is saturated or consumers suffer fromtedium with repetitive advertising.

The responsiveness of sales to advertisingis the rate of change in sales as we changeadvertising. It is captured by the slope of thecurve in Figure 24.2 or the coefficient of themodel used to estimate the curve. This coeffi-cient is generally represented as β in Equation(1). Just as we expect the advertising sales curveto follow a certain shape, we also expect thisresponsiveness of sales to advertising to showcertain characteristics. First, the estimatedresponse should preferably be in the form ofan elasticity. The elasticity of sales to advertis-ing (also called advertising elasticity, in short)is the percentage change in sales for a 1%change in advertising. So defined, an elasticityis units-free and does not depend on the mea-sures of advertising or of sales. Thus, it is a puremeasure of advertising responsiveness whosevalue can be compared across products, firms,markets, and time. Second, the elasticity shouldneither always increase with the level of adver-tising nor be always constant but should showan inverted bell-shaped pattern in the level ofadvertising. The reason is the following.

Linear Response

Sales

Advertising

Concave Response

S-Shaped Response

Figure 24.2 Linear and Nonlinear Response to Advertising



We would expect responsiveness to be lowat low levels of advertising because it would bedrowned out by the noise in the market. Wewould expect responsiveness to be low also atvery high levels of advertising because of satu-ration. Thus, we would expect the maximumresponsiveness of sales at moderate levels ofadvertising. It turns out that when advertisinghas an S-shaped response with sales, theadvertising elasticity would have this invertedbell-shaped response with respect to advertis-ing. So the model that can capture the S-shapedresponse would also capture advertising elastic-ity in its theoretically most appealing form.

Competitive Effects

Advertising normally takes place in freemarkets. Whenever one brand advertises a suc-cessful innovation or successfully uses a newadvertising form, other brands quickly imitateit. Competitive advertising tends to increase thenoise in the market and thus reduce the effec-tiveness of any one brand’s advertising. Thecompetitive effect of a target brand’s advertisingis its effectiveness relative to that of the otherbrands in the market. Because most advertisingtakes place in the presence of competition, try-ing to understand advertising of a target brand inisolation may be erroneous and lead to biasedestimates of the elasticity. The simplest methodof capturing advertising response in competitionis to measure and model sales and advertising ofthe target brand relative to all other brands in themarket.

In addition to just the noise effect of com-petitive advertising, a target brand’s advertisingmight differ due to its position in the market orits familiarity with consumers. For example,established or larger brands may generally getmore mileage than new or smaller brands fromthe same level of advertising because of thebetter name recognition and loyalty of the for-mer. This effect is called differential advertisingresponsiveness due to brand position or brandfamiliarity.

Dynamic Effects

Dynamic effects are those effects of advertis-ing that change with time. Included under this

term are carryover effects discussed earlier andwearin, wearout, and hysteresis discussed here.To understand wearin and wearout, we need toreturn to Figure 24.2. Note that for the concaveand the S-shaped advertising response, salesincrease until they reach some peak as advertisingintensity increases. This advertising responsecan be captured in a static context—say, the firstweek or the average week of a campaign.However, in reality, this response pattern changesas the campaign progresses.

Wearin is the increase in the response of salesto advertising, from one week to the next ofa campaign, even though advertising occurs atthe same level each week (see Figure 24.3).Figure 24.3 shows time on the x-axis (say inweeks) and sales on the y-axis. It assumes anadvertising campaign of 7 weeks, with one expo-sure per week at approximately the same timeeach week. Notice a small spike in sales witheach exposure. However, these spikes keepincreasing during the first 3 weeks of the cam-paign, even though the advertising level is thesame. That is the phenomenon of wearin. Indeed,if it at all occurs, wearin typically occurs at thestart of a campaign. It could occur because repe-tition of a campaign in subsequent periodsenables more people to see the ad, talk about it,think about it, and respond to it than would havedone so on the very first period of the campaign.

Wearout is the decline in sales response ofsales to advertising from week to week of acampaign, even though advertising occurs at thesame level each week. Wearout typically occursat the end of a campaign because of consumertedium. Figure 24.3 shows wearout in the last 3weeks of the campaign.

Hysteresis is the permanent effect of an adver-tising exposure that persists even after the pulseis withdrawn or the campaign is stopped (seeFigure 24.1D). Typically, this effect does notoccur more than once. It occurs because an adestablished a dramatic and previously unknownfact, linkage, or relationship. Hysteresis is anunusual effect of advertising that is quite rare.

Content Effects

Content effects are the variation in responseto advertising due to variation in the contentor creative cues of the ad. This is the most

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important source of variation in advertisingresponsiveness and the focus of the creativetalent in every agency. This topic is essentiallystudied in the field of consumer behavior usinglaboratory or theater experiments. However,experimental findings cannot be easily andimmediately translated into management prac-tice because they have not been replicated in thefield or in real markets. Typically, modelershave captured the response of consumers ormarkets to advertising measured in the aggre-gate (in dollars, gross ratings points, or expo-sures) without regard to advertising content. Sothe challenge for modelers is to include mea-sures of the content of advertising when model-ing advertising response in real markets.

Media Effects

Media effects are the differences in advertis-ing response due to various media, such as TV

or newspaper, and the programs within them,such as channel for TV or section or story fornewspaper.

MODELING ADVERTISING RESPONSE

This section discusses five different models ofadvertising response, which address one or moreof the above effects. Some of these models areapplications of generic forms presented inChapters 12, 13, and 14. The models are pre-sented in the order of increasing complexity. Bydiscussing the strengths and weaknesses of eachmodel, the reader will appreciate its value andthe progression to more complex models. Bycombining one or more models below, aresearcher may be able to develop a model thatcan capture many of the effects listed above.However, that task is achieved at the cost of greatcomplexity. Ideally, an advertising model should

Sales

Base Sales

Time in Weeks

Advertising Wearout

Advertising Wearin

Ad Exposures (one per week)

Figure 24.3 Wearin and Wearout in Advertising Effectiveness


be rich enough to capture all the seven effectsdiscussed above. No one has proposed a modelthat has done so, though a few have come close.

Basic Linear Model

The basic linear model can capture the firstof the effects described above, the current effect.The model takes the following form:

Yt = α + β1 At + β2Pt + β3Rt + β4Qt + εt.

Here, Y represents the dependent variable (e.g.,sales), while the other capital letters represent vari-ables of the marketing mix, such as advertising(A), price (P), sales promotion (R), or quality (Q).The parameters α and βk are coefficients that theresearcher wants to estimate. βk represents theeffect of the independent variables on the depen-dent variable, where the subscript k is an index forthe independent variables. The subscript t repre-sents various time periods. A section below dis-cusses the problem of the appropriate time interval,but for now, the researcher may think of time asmeasured in weeks or days. The εt are errors in theestimation of Yt that we assume to independentlyand identically follow a normal distribution (IIDnormal). This assumption means that there is nopattern to the errors so that they constitute just ran-dom noise (also called white noise). Our simplemodel assumes we have multiple observations(over time) for sales, advertising, and the othermarketing variables. This model can best be esti-mated by regression, a simple but powerful statisti-cal tool discussed in Chapter 13. While simple, thismodel can only capture the first of the seven effectsdiscussed above.

Multiplicative Model

The multiplicative model derives its namefrom the fact that the independent variables ofthe marketing mix are multiplied together. Thus,

Yt = Exp(α) × Atβ1 × Pt

β2 × Rtβ3 × Qt

β4 × εt.

While this model seems complex, a simpletransformation can render it quite simple. In particu-lar, the logarithmic transformation linearizes Equa-tion (3) and renders it similar to Equation (2); thus,

log (Yt) = α + β1 log(At) + β2 log(Pt) +β3 log(Rt) + β4 log(Qt) + εt.

The main difference between Equation (2) andEquation (4) is that the latter has all variables asthe logarithmic transformation of their originalstate in the former. After this transformation, theerror terms in Equation (4) are assumed to beIID normal.

The multiplicative model has many benefits.First, this model implies that the dependentvariable is affected by an interaction of the vari-ables of the marketing mix. In other words, theindependent variables have a synergistic effecton the dependent variable. In many advertisingsituations, the variables could indeed interact tohave such an impact. For example, higher adver-tising combined with a price drop may enhancesales more than the sum of higher advertising orthe price drop occurring alone.

Second, Equations (3) and (4) imply thatresponse of sales to any of the independent vari-ables can take on a variety of shapes dependingon the value of the coefficient. In other words,the model is flexible enough that it can capturerelationships that take a variety of shapes byestimating appropriate values of the responsecoefficient.

Third, the β coefficients not only estimatethe effects of the independent variables on thedependent variables, but they are also elasticities.Estimating response in the form of elasticitieshas a number of advantages listed above.

However, the multiplicative model hasthree major limitations. First, it cannot estimatethe latter five of the seven effects describedabove. For this purpose, we have to go to othermodels. Second, the multiplicative model isunable to capture an S-shaped response of adver-tising to sales. Third, the multiplicative modelimplies that the elasticity of sales to advertisingis constant. In other words, the percentage rate atwhich sales increase in response to a percentageincrease in advertising is the same whatever thelevel of sales or advertising. This result is quiteimplausible. We would expect that percentageincrease in sales in response to a percentageincrease in advertising would be lower as thefirm’s sales or advertising become very large.Equation (4) does not allow such variation in theelasticity of sales to advertising.


(2)

(3)

(4)


Exponential Attraction andMultinomial Logit Model

Attraction models are based on the premisethat market response is the result of the attractivepower of a brand relative to that of other brandswith which they compete. The attraction modelimplies that a brand’s share of market sales is afunction of its share of total marketing effort; thus,

Mi = Si /∑

jSj = Fi /∑

jFj,

Here, Mi is the market share of the ith brand(measured from 0 to 1), Si is the sales of brandi,

∑j implies a summation of the values of the

corresponding variable over all the j brands inthe market, and Fi is brand i’s marketing effortand is the effort expended on the marketingmix (advertising, price, promotion, quality, etc.).Equation (5) has been called Kotler’s funda-mental theorem of marketing. Also, the right-hand-side term of Equation (5) has been calledthe attraction of brand i. Attraction modelsintrinsically capture the effects of competition.

A simple but inaccurate form of the attrac-tion model is the use of the relative form ofall variables in Equation (2). So for sales, theresearcher would use market share. For adver-tising, he or she would use share of advertisingexpenditures or share of gross rating points(share of voice) and so on. While such a modelwould capture the effects of competition, itwould suffer from other problems of the linearmodel, such as linearity in response. Also, it isinaccurate because the right-hand side wouldnot be exactly the share of marketing effort butthe sum of the individual shares of effort oneach element of the marketing mix.

A modification of the linear attraction modelcan resolve the problem of linearity in responseand the inaccuracy in specifying the right-handside of the model plus provide a number of otherbenefits. This modification expresses the marketshare of the brand as an exponential attraction ofthe marketing mix; thus,

Mi = Exp (Vi ) /∑

j Exp Vj,

where Mi is the market share of the ith brand(measured from 0 to 1), Vj is the marketingeffort of the jth brand in the market,

∑j stands

for summation over the j brands in the market,

Exp stands for exponent, and Vi is the marketingeffort of the ith brand, expressed as the right-hand side of Equation (2). Thus,

Vi = α + β1 Ai + β2Pi + β3Ri + β4Qi + ei,

where ei are error terms. By substituting thevalue of Equation (7) in Equation (6), we get

Mi = Exp (Vi)/∑

j Exp Vj = Exp(∑

kβk Xik + ei)/∑j Exp(

∑kβk Xik + ej),

where Xk (0 to m) are the m independentvariables or elements of the marketing mix,and α = β0 and Xi0 = 1. The use of the ratio ofexponents in Equations (6) and (8) ensuresthat market share is an S-shaped function ofshare of a brand’s marketing effort. As such, ithas a number of nice features discussed earlier.

However, Equation (8) also has two limita-tions. First, it is not easy to interpret because theright-hand side of Equation (8) is in the formof exponents. Second, it is intrinsically nonlin-ear and difficult to estimate because the denom-inator of the right-hand side is a sum of theexponent of the marketing effort of each brandsummed over each element of the marketingmix. Fortunately, both of these problems can besolved by applying the log-centering transfor-mation to Equation (8) (Cooper & Nakanishi,1988). After applying this transformation,Equation (8) reduces to

Log(MiM−) = α*

i + ∑kβk(X *

ik) + e*i ,

where the terms with * are the log-centeredversion of the normal terms; thus, α*

i = αi − α− ,X *

ik = Xik − X−

i , e*i = ei − e−, for k = 1 to m, and the

terms with are the geometric means of the nor-mal variables over the m brand in the market.

The log-centering transformation ofEquation (8) reduces it to a type of multinomiallogit model in Equation (9). The nice feature ofthis model is that it is relatively simpler, moreeasily interpreted, and more easily estimatedthan Equation (8). The right-hand side ofEquation (9) is a linear sum of the transformedindependent variables. The left-hand side ofEquation (9) is a type of logistic transformationof market share and can be interpreted as the logodds of consumers as a whole preferring the


(5)

(6)

(7)

(8)

(9)


target brand relative to the average brand in themarket.

The particular form of the multinominal logitin Equation (9) is aggregate. That is, this form isestimated at the level of market data obtainedin the form of market shares of the brand and itsshare of the marketing effort relative to the otherbrands in the market. An analogous form of themodel can be estimated at the level of an individ-ual consumer’s choices (e.g., Tellis, 1988a). Thisother form of the model estimates how individualconsumers choose among rival brands and iscalled the multinomial logit model of brand choice(Guadagni & Little, 1983). Chapter 14 covers thischoice model in more detail than done here.

The multinomial logit model (Equation (9))has a number of attractive features that render itsuperior to any of the models discussed above.First, the model takes into account the competi-tive context, so that predictions of the model aresum and range constrained, just as are the origi-nal data. That is, the predictions of the marketshare of any brand range between 0 and 1, andthe sum of the predictions of all the brands inthe market equals 1.

Second, and more important, the functionalform of Equation (6) (from which Equation (9)is derived) suggests a characteristic S-shapedcurve between market share and any of the inde-pendent variables (see Figure 24.2). In the caseof advertising, for example, this shape impliesthat response to advertising is low at levels ofadvertising that are very low or very high. Thischaracteristic is particularly appealing basedon advertising theory. The reason is that verylow levels of advertising may not be effectivebecause they get lost in the noise of competingmessages. Very high levels of advertising maynot be effective because of saturation or dimin-ishing returns to scale. If the estimated lowerthreshold of the S-shaped relationship doesnot coincide with 0, this indicates that marketshare maintains some minimal floor level evenwhen marketing effort declines to a zero. Wecan interpret this minimal floor to be the baseloyalty of the brand. Alternatively, we can inter-pret the level of marketing effort that coincideswith the threshold (or first turning point) of theS-shaped curve as the minimum point necessaryfor consumers or the market to even notice achange in marketing effort.

Third, because of the S-shaped curve ofthe multinomial logit model, the elasticity ofmarket share to any of the independent variablesshows a characteristic bell-shaped relationshipwith respect to marketing effort. This relation-ship implies that at very high levels of marketingeffort, a 1% increase in marketing effort trans-lates into ever smaller percentage increases inmarket share. Conversely, at very low levelsof marketing effort, a 1% decrease in market-ing effort translates into ever smaller percentagedecreases in market share. Thus, market shareis most responsive to marketing effort at someintermediate level of market share. This pattern iswhat we would expect intuitively of the relation-ships between market share and marketing effort.

Despite its many attractions, the exponentialattraction or multinomial model as definedabove does not capture the latter four of theseven effects identified above.

Koyck and Distributed Lag Models

The Koyck model may be considered asimple augmentation of the basic linear model(Equation (2)), which includes the laggeddependent variable as an independent variable.What this specification means is that salesdepend on sales of the prior period and all theindependent variables that caused prior sales,plus the current values of the same independentvariables.

Yt = α + λYt − 1 + β1At + β2Pt + β3Rt + β4Qt + εt.

(10)

In this model, the current effect of advertisingis β1, and the carryover effect of advertisingis β1λ / (1 − λ). The higher the value of λ, thelonger the effect of advertising. The smaller thevalue of λ, the shorter the effects of advertis-ing, so that sales depend more on only currentadvertising. The total effect of advertising isβ1 / (1 − λ).

While this model looks relatively simple andhas some very nice features, its mathematicscan be quite complex (Clarke, 1976). Moreover,readers should keep in mind the following limi-tations of the model. First, this model can cap-ture carryover effects that only decay smoothlyand do not have a hump or a nonmonotonic



decay. Second, estimating the carryover of anyone variable is quite difficult when there aremultiple independent variables, each with itsown carryover effect. Third, the level of dataaggregation is critical. The estimated durationof the carryover increases or is biased upwardsas the level of aggregation increases. A recentpaper has proved that the optimal data intervalthat does not lead to any bias is not the inter-purchase time of the category, as commonlybelieved, but the largest period with at most oneexposure and, if it occurs, does so at the sametime each period (Tellis & Franses, in press).

The distributed lag model is a model withmultiple lagged values of both the dependentvariable and the independent variable. Thus,

Yt = α + λ1Yt – 1 + λ2Yt – 2 + λ3Yt – 3 + . . .+ β10At + β11At − 1 + β12At − 2 + . . .+ β2Pt + β3Rt + β4Qt + εt.

This model is very general and can capturea whole range of carryover effects. Indeed, theKoyck model can be considered a special caseof distributed lag model with only one laggedvalue of the dependent variable. The distributedlag model overcomes two of the problems withthe Koyck model. First, it allows for decay func-tions, which are nonmonotonic or humpedshaped (see Figure 24.4). Second, it can partlyseparate out the carryover effects of differentindependent variables. However, it also suffersfrom two limitations. First, there is considerablemulticollinearity between lagged and currentvalues of the same variables. Second, because ofthis problem, estimating how many lagged vari-ables are necessary is difficult and unreliable.Thus, if the researcher has sufficient extensivedata that minimize the latter two problems, thenhe or she should use the distributed laggedmodel. Otherwise, the Koyck model would be areasonable approximation.

Hierarchical Models

The remaining effects of advertising that weneed to capture (content, media, wearin, andwearout) involve changes in the responsivenessitself of advertising (i.e., the β coefficient) dueto advertising content, media used, or time of acampaign. These effects can be captured in one

of two ways: dummy variable regression or ahierarchical model.

Dummy variable regression is the use ofvarious interaction terms to capture how adver-tising responsiveness varies by content, media,wearin, or wearout. We illustrate it in the con-text of a campaign with a few ads. First, supposethe advertising campaign uses only a few differ-ent types of ads (say, two). Also, assume we startwith the simple regression model of Equation(3). Then we can capture the effects of thesedifferent ads by including suitable dummy vari-ables. One simple form is to include a dummyvariable for the second ad, plus an interactioneffect of advertising times this dummy variable.Thus,

Yt = α + β1At + δAt A2t +β2Pt + β3Rt + β4Qt + εt,

where A2t is a dummy variable that takes onthe value of 0 if the first ad is used at time t andthe value of 1 if the second ad is used at time t.δ is the effect of the interaction term (AtA2t).In this case, the main coefficient of advertis-ing, β1, captures the effect of the first ad, whilethe coefficients of β1 plus that of the interactionterm (δ) capture the effect of the second ad.While simple, these models quickly becomequite complex when we have multiple ads,media, and time periods, especially if these areoccurring simultaneously. This is the situationin real markets. The problem can be solved bythe use of hierarchical models.

Hierarchical models are multistage modelsin which coefficients (of advertising) estimatedin one stage become the dependent variable inthe other stage. The second stage contains thecharacteristics by which advertising is likelyto vary in the first stage, such as ad content,medium, or campaign duration. Consider thefollowing example.

Example

A researcher gathers data about the effect ofadvertising on sales for a brand of one firm overa 2-year period. The firm advertises the brandusing a large number of different ads (or copycontent), in campaigns of varying duration (say, 2to 8 weeks), in a number of different cities or


(11)(12)



markets. Assume that the researcher has data ata highly disaggregate level, say the hour of theday. Such data are possible because of electronicdatabases such as that recorded by Internet retail-ers, telemarketers, or retail firms with scanners.The researcher analyzes the effect of advertisingon sales, separately for each city, campaign (ad),and week of the campaign. These effects varysubstantially across the various estimations of themodel. Why do they vary?

The researcher suspects that the variationcould be due to varying responsiveness inmarkets, or by campaign, or by week of thecampaign. The researcher has information on allthese three factors (market, campaign, and weekof campaign). Then in a second-stage model, theresearcher can analyze how the coefficients ofadvertising estimated in the first stage vary dueto these three factors. The dependent variable isthe coefficients of advertising from the first stage,and the independent variables are the factors that

gave rise to that coefficient. Such amultistage model is called a hierarchical model(e.g., Chandy, Tellis, MacInnis, & Thaivanich,2001; Tellis, Chandy, & Thaivanich, 2000).

Two features are essential for hierarchicalmodels. First, we should be able to obtainmultiple estimates of the effects (or coefficientvalues) of advertising on some dependent vari-able such as sales or market share for the samebrand across different contexts such as at leastone of the following: the ad campaign, week ofthe campaign, market, or medium. Then we canuse the estimates of the effects of advertisingfrom the first stage as dependent variables in thesecond stage. Second, as far as possible, weneed to minimize excessive covariation amongfactors. Thus, a particular ad should not alwaysoccur with a particular channel, or an ad of aparticular duration should not always be run ina particular channel. Such co-occurrence leadsto the problem of multicollinearity among the

Sales

Koyck Model:Sales = functionof lagged sales

Sales = function oftwice-lagged salesand advertising

Sales = function oftwice-lagged sales,advertising, andlagged advertising

Time

Advertising Exposures

Figure 24.4 Alternate Shapes of Advertising Carryover


created variables in the second-stage model(see Chapter 13). As long as the three factorshave sufficient cross-variation, estimates of thesecond-stage model should be reliable.

Depending on the richness of the data, hierar-chical models can estimate the last three effectsof advertising that we identified above. That is,with such models and given suitable data, theresearcher can estimate what ad content is themost effective, what duration of the campaign isthe most effective, and which media are the mosteffective. The duration of the campaign could beestimated in terms of weeks. For example, if theeffectiveness of the ad first increases slowlyand then decreases suddenly, one could concludethat wearin is slow but wearout is rapid. On theother hand, if the effectiveness of the ad steadilydeclines over time, then there is no wearin, andwearout sets out from the start. Furthermore, ifthe data are sufficiently rich and detailed, theresearcher can also obtain interaction effectssuch as which media are most suitable for par-ticular ads or which ad content needs to be runover campaigns of long versus short duration.

Note that to address all of the seven effectsof advertising identified above, the researcherwould have to use a hierarchical model, whichitself contains an exponential attraction ormultinomial logit model with a Koyck-type ordistributed lag enhancement. In other words,suitably integrating models described abovewould enable a researcher to address the mostimportant phenomena associated with advertis-ing. In reality, such fully integrated models thatcan capture all the effects of advertising are verycomplex and require substantial data (e.g., seeChandy et al., 2001). If researchers want to focuson only a few effects or their data are not rich,they might want to simplify the model they useto focus on only the most important effects.

PATTERNS AND

MODELS OF PRICE RESPONSE

The first four effects of advertising responsealso apply to price: current, shape, competition,and carryover effects. The current effect ofprice is the changes in sales that occur in thesame period as that in which prices change. Incontrast to response to advertising, response to

price is typically strong and immediate, withmost of the effect lasting in the current period(Sethuraman & Tellis, 1991).

However, price changes can also have carry-over effects. These effects could occur becauseconsumers take time to learn of the pricechange, wait to respond until their next shop-ping trip, or wait to respond because of theircurrent inventory. Typically, carryover effectsare less pronounced for price than for advertis-ing. One type of carryover is the negative salesfollowing a price cut, because consumers buyexcess stock during the discount and then holdback regular purchases until they deplete theirstocks.

The exponential attraction or multinomiallogit model specified for advertising responsealso serves very well to capture S-shapedresponse and competitive effects, if any, inresponse to pricing. In addition, the integrationof these models with a Koyck or distributed lagspecification can capture any carryover effectsthat may exist in response to pricing.

In addition, response to price has three moreeffects that are unique to price: promotionalprice effect, reference price effect, and priceinteraction effect. To capture the three effects,the researcher has merely to modify the linear,multinomial logit, or distributed lag model byincluding relevant independent variables. Thebasic structure of the model need not change.Thus, in the interests of parsimony, here we dis-cuss only the unique effects of pricing and howmodifications of the classic models discussedabove can capture these effects.

Modeling Promotion Price Effect

A pervasive feature of pricing in contempo-rary markets is that prices are constantly in flux.Retailers have a certain list price, and frequentlyfor a variety of reasons, they offer discounts or“sales” from these prices (Tellis, 1986). Thus,pricing strategies have two components: (1) a listprice component that is basically how a brand islisted on price relative to other brands and (2) apromotion price component, which basicallyinvolves a temporary discount off this list price.So, models of response to pricing should containboth of these components to correctly specifyand fully capture all the effects of price.




Assume one has chosen the multinominallogit model discussed above. Then, to fully cap-ture the promotional price effect, one would usetwo independent variables for price, instead ofonly one: One variable would represent the listprice of the brand; the other variable would rep-resent the promotion price of the brand. The keyquestion would be how to measure the list andpromotion price.

In markets today, firms generally keep the listprice of the brand high for an extended period oftime but occasionally drop its price by offering asales or discount (Tellis, 1998). Thus, one candefine and capture the list price as the highmodal price of the brand over a given time hori-zon (see Figure 24.5). One can define the pro-motional price or discount of the brand as the listprice minus the actual price charged or paid in aparticular time period within that horizon. Onewould use the same rules to compute the list andpromotional prices for competing brands.

The estimated coefficients (elasticities) ofthese variables would then reflect the responseof markets to these respective variables. By theirdefinition, the effect of the list price would gen-erally be negative. That is, the higher the listprice of the brand, the lower its sales or marketshare. The effect of the promotional price wouldgenerally be positive. That is, the steeper thepromotional discount of the brand, the higher itssales or market share.

Modeling Reference Price Effect

Reference prices are latent internal normsthat consumers use as a basis against which tocompare current prices (Tellis, 1998; Winer,1986). Reference prices are not observed andcannot be ascertained by survey because of theproblem of demand bias. Even if they did notexist, consumers would be tempted to answer inthe affirmative about them just to please theresearcher. The best way to test for referenceprices is by the prediction of behavior withand without reference prices. For example, aresearcher can ascertain a model’s improvementin fit with the data, if any, from the inclusion ofterms that capture reference price.

Current research suggests at least two com-ponents of reference price (Rajendran & Tellis,1994): first, a temporal or internal referenceprice based on memory that probably developsin response to past prices a consumer has paidand, second, an external or contextual referenceprice based on visible prices that probablyrelates to the prices of other competing brandsavailable to the consumer at the time of pur-chase. A complete model of response to pricingshould capture these effects of reference price.Any of the models discussed above can accountfor reference price effects by including indepen-dent variables for these effects. In effect, insteadof a single variable for price, the researcher

Price

List Price

Discounts

Time

Figure 24.5 Price Path of One Brand in One Store Over Time


would include a variable for the temporalreference price minus price paid, plus anothervariable for the contextual reference price minusprice paid. The next problem is how exactly tomeasure these reference prices.

To measure the contextual reference price of atarget brand, the researcher could use either oneof the average of the other brands’ prices or thelowest among the other brands’prices or the priceof the leading rival brand (Rajendran & Tellis,1994). The other or rival brands being consideredin this case are those with which the target brandis available. Which of these three prices aresearcher uses depends on which price is mostsalient to consumers when they make decisionsbased on price. In the absence of a strong theoryabout this issue, a researcher would try out eachof these three reference prices and use the onethat gives the best fit with the data.

To capture the temporal reference price, theresearcher would use some moving average ofpast prices that the consumer has used for thetarget brand. Instead of a simple average, someresearchers advocate a weighted moving aver-age of past prices. The key issue here is, howdoes one estimate the weights and the numbersof prior periods that should be included in thedefinition? The current thinking is that oneshould fit a time-series model that best capturesthe string of past prices for a brand (Winer,1986). The logic for this thinking is that theprices that can best be predicted are those that aconsumer is mostly likely to be able to recollectand respond to. However, there is no absoluterule that any one measure of past prices is thebest for the temporal reference price compo-nent. In effect, a researcher would use that com-ponent that he or she finds to fit the data best.

Modeling Promotional andReference Price Effects Jointly

A model can get quite unwieldy if oneattempts to capture both promotional and refer-ence price effects and, for each of these, captureboth temporal and contextual components.Fortunately, reference price effects are probablyrelated to promotional price effects. In particu-lar, list prices are more likely to need a contex-tual or external reference price. The reason isthat list prices do not change much over time, so

consumers probably form them from the listprices of competing brands at the point of pur-chase. On the other hand, promotional prices aremore likely to be compared to a temporal orinternal reference price because they vary overtime and depend on consumer memory andexperience of these prices.

Thus, despite many pricing effects, a resear-cher might capture most of these effects parsi-moniously with just two independent variablesfor price. The first variable would be the refer-ence list price minus the actual list price. Thisterm would capture the effect of list prices rela-tive to contextual reference prices. The secondterm would be the temporal reference discountminus the discount actually obtained. This termwould capture the effect of discounts with regardto temporal reference prices. The discount itselfis the list price minus the actual price paid at anyone period.

Modeling Interaction Effects

Often, marketing variables affect consumerssynergistically. That is, the effect of two of themtogether is greater than the sum of the effect ofeach of them separately. We refer to this syner-gistic effect as an interaction effect. One mightargue that the whole concept of the marketingmix is that these variables do not act alone buthave some joint effect that is much greater thanthe sum of the parts. The general way in whichresponse models capture interaction effects is byincluding an additional term that is formed bythe product of the two variables that interact.For example, if the researcher believes thatadvertising would be more effective during thetime of a discount, the researcher would includea new independent variable formed from themultiplication of advertising and discounts.

When one already has a large number of inde-pendent variables, some of which have multiplecomponents (such as lagged values of advertis-ing or temporal and contextual reference prices),then testing out all sorts of interactions canget quite complex. What is needed is a modelthat can do so parsimoniously. Some of the pastmodels may do so under certain assumptions.

Consider the multiplicative model inEquation (3). This model in its original form(with all the variables measured naturally)



implies that sales result from the multiplicativemix of the independent variables. In other words,it assumes that sales result from the interactionof the marketing mix. However, in its logarith-mic form (after taking logs of all the variables)in Equation (4), which is used to linearize andestimate the model, it no longer contains inter-action effects. So if theory suggests that theinteraction effects hold in the natural state ofthe variables but not in their logarithmic state,then the multiplicative model serves as a parsi-monious means of capturing those interactioneffect. Alternatively, if the researcher believesthat the interaction effects persist even aftertaking logs of the natural variables or if theresearcher is not sure, he or she could just run amodel that includes additional interaction termsof the log of the marketing variables suspected tohave interaction effects.

If the researcher has reason to believe thata strong interaction effect exists between somevariables and the researcher is using a model otherthan the multiplicative model, then he orshe is best advised to model the interactioneffect explicitly. This modeling can be achievedby including an additional independent variableformed by multiplication of those variables thatthe researcher assumes do interact with each other.

A PARTIALLY INTEGRATED HIERARCHICAL

MODEL FOR AD RESPONSE

No researcher has published a model thatcaptures all of the seven characteristics ofmarketing-mix models. However, a recentexample published in two studies by a teamof four authors shows how one could captureall of these effects except competition. Now,many readers will argue that competition ispervasive in markets today and is the mostimportant dimension to capture. However, inthis particular example, competitors were notpresent. Also, advertising was the only elementof the marketing mix that the firm used. Giventhese two caveats, the authors were able tointegrate the other six desirable characteristicsof marketing models quite nicely.

This example is due to a study done byTellis et al. (2000) and Chandy et al. (2001).The researchers have referrals (sales) and TV

advertising data for a referral service over severalyears across more than 30 cities. In each city, theservice provider can draw from a bank of about70 creatives developed over the years. Fortu-nately, the firm uses different creatives in differ-ent cities, in each of which the firm has operatedfor a varying length of time. The researchers wereable to describe the differences in those creativesby a set of key characteristics, such as the use ofemotion, argument, endorser, certain types ofcopy, and so on. They were also able to calibratedifferences in the various cities by the age of themarket at which time the ad was aired.

Given this scenario, a first-stage model couldexplain what effects each creative has in eachcity. Then, a second-stage model can explain howthose effects vary by type of creatives and typeof city. This is a hierarchical model. We nowproceed to describe the equations in each stage.

Stage 1: EstimatingResponse to Ads (Creatives)

The authors began with a distributed lagmodel such as that in Equation (11). The authorsthen included a dummy variable in the modelfor the presence or absence of each creative. Thecoefficient of this variable determines how theeffect of advertising varies from the commoneffect captured in Equation (11) due to the useof a particular creative and the age of the marketat that time. The authors also included manycontrol variables to account for other differ-ences, such as hour of the day and day of theweek when the sales occurred, the station andday-part (morning or evening) in which the adaired, and whether the service was open.

The first-stage model is

R = α + (R−lλ + AβA + Cβc + SβS + SHβSH

+ HDβHD + AMβM) O + εt,

where

R = a vector of referrals by hour,

R−l = a matrix of lagged referrals by hour,

A = a matrix of current and lagged ads by hour,

C = a matrix of dummy variables indicatingwhether a creative is used in each hour,1

S = a matrix of current and lagged ads in each TVstation by hour,


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AM = a matrix of current and lagged morning adsby hour,

H = a matrix of dummy variables for time of dayby hour,

D = a matrix of dummy variables for day of weekby hour,

O = a vector of dummies recording whether theservice is open by hour,

α = constant term to be estimated,

λ = a vector of coefficients to be estimated forlagged referrals,

βi = vectors of coefficients to be estimated, and

εt = a vector of error terms initially assumed to beIID normal.

Note that in this study, the authors are able tocapture many of the key effects of advertising.For example, βA captures the main effect ofadvertising by hour of the day. A combination ofλ and βA captures the carryover effect of adver-tising. βc captures the effects of various creativesthat were used, plus the main effects of advertis-ing by hour of the day. βS captures the effect ofthe various media (TV stations) that were used.

Note that the authors included the creativesas dummy variables in Equation (13), indicatingwhether a creative is used in a particular market.They chose to drop the creatives that had anaverage effectiveness and to include only thosethat were significantly above or below theaverage. Thus, the coefficient of a creative inEquation (13) represents the increase or decreasein expected referrals due to that creative, relativeto the average of creatives in that particularmarket. This specification had the most practicalrelevance. Managers are not interested much ina global optimization of the best mix of cre-atives. Rather, they are interested in makingimprovements over their strategy in the previousyear. For this reason, they seek analyses thathighlight the best creatives (to use more often)or the worst creatives (to drop).

The results showed that although advertisinghas small effects, these effects varied dramati-cally by type of ad and TV channel. Thus, man-agers could drop the least effective ads and TVchannels and spend more on the most effectiveads and TV channels. The detailed data and spec-ification of the model revealed a number of otherinteresting phenomena about how advertising’s

effects vary and decay by time of the day and dayof the week.

Stage 2: Explaining Effectivenessof Ad Response by Type of Creative

In the second stage, the authors collected thecoefficients (βc) for each creative for each market(m) in which it is used and explained their varia-tion as a function of creative characteristics andthe age of the market in which it ran as follows:

βc,m = ϕ1 Argumentc + ϕ2 (Argumentc × Agem)+ ϕ3Emotionc + ϕ4 (Emotionc × Agem)+ ϕ5800 Visiblec + ϕ6 (800 Visiblec

× Agem) + ϕ7Negativec + ϕ8 (Negativec

× Agem) + ϕ9Positivec + ϕ10

(Positivec × Agem) + ϕ11Expertc + ϕ12

(Expertc × Agem) + ϕ13Nonexpertc + ϕ14

(Nonexpertc × Agem) + ϕ15Agem + ϕ16

(Agem)2 + ΓΓ Market + v,

where

βc,m = coefficients of creative c in market m fromEquation (13),

Age = market age (number of weeks since theinception of service in the market),

Market = matrix of market dummies,

ΓΓ == vector of market coefficients,

v = vector of errors,

ϕ = second-stage coefficients to be estimated, andother variables are as defined in Equation (4).

The characteristics of creatives that wereparticularly important were the use of argument,emotion, expert endorsers, visibility of the brandname, negative versus positive arguments, andexpert versus nonexpert endorsers. The authors’most important finding was that emotionalappeals were effective in mature markets whileargument appeals were effective in new markets.Furthermore, a nonlinear regression of the effec-tiveness of ads on the age of the creatives enabledthe researchers to assess the effects of wearin andwearout. They found that ads have no wearinperiod, and wearout starts from the very firstweek of the campaign and is steepest in the firstfew weeks. Thus, frequently changing campaignsand developing new campaigns would be veryuseful. When developing new campaigns, usingappeals that were the most effective for the age ofthe market would be highly advisable.


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CONCLUSION

Planning the marketing mix is a central taskin marketing management. Prudent planningrequires that marketing managers take intoaccount how markets have responded to themarketing mix in the past. The underlyingassumption is not that the past predicts thefuture with certainty but that it contains valuablelessons that might enlighten the future.

The econometrics of response modelingdescribes how a researcher should modelresponse to the marketing mix so as to capturethe most important effects validly. This chapterprovides an overview of the essential issues andprinciples in this area. It first describes theimportant effects that occur in markets today. Itthen discusses the strengths and limitations ofvarious models that capture those effects.

The chapter focuses on two elements ofthe marketing mix: advertising and pricing. Thisfocus is because the variables are the most com-monly managed and analyzed and encompass awide range of response patterns. Understandinghow to model response to these two variablesshould provide researchers with the essentialtools to model response to other elements of themarketing mix. The chapter provides referencesto articles and chapters of this book that providefurther details on these issues.

NOTE

1. We use C to refer to the matrix of creativeshere and c to refer to individual creatives later in thechapter.

REFERENCES

Chandy, R., Tellis, G. J., MacInnis, D., & Thaivanich,P. (2001). What to say when: Advertising appealsin evolving markets. Journal of MarketingResearch, 38, 399–414.

Clarke, D. G. (1976). Econometric measurement ofthe duration of advertising effect on sales.Journal of Marketing Research, 13, 345–357.

Cooper, L. G., & Nakanishi, M. (1988). Market shareanalysis. Norwell, MA: Kluwer.

Guadagni, P., & Little, J. D. C. (1983). A logit modelof brand choice calibrated on scanner data.Marketing Science, 2, 203–238.

McCarthy, J. (1996). Basic marketing: A managerialapproach (12th ed.). Homewood, IL: Irwin.

Rajendran, K. N., & Tellis, G. J. (1994). Is referenceprice based on context or experience? An analy-sis of consumers’ brand choices. Journal ofMarketing, 58, 10–22.

Sethuraman, R., & Tellis, G. J. (1991). An analysis ofthe tradeoff between advertising and pricing.Journal of Marketing Research, 31, 160–174.

Tellis, G. J. (1986). Beyond the many faces of price:An integration of pricing strategies. Journal ofMarketing, 50, 146–160.

Tellis, G. J. (1988a). Advertising exposure, loyalty andbrand purchase: A two-stage model of choice.Journal of Marketing Research, 15, 134–144.

Tellis, G. J. (1988b). The price sensitivity of compet-itive demand: A meta-analysis of sales responsemodels. Journal of Marketing Research, 15,331–341.

Tellis, G. J. (1989). Interpreting advertising andprice elasticities. Journal of AdvertisingResearch, 29(4), 40–43.

Tellis, G. J. (1998). Advertising and sales promotionstrategy. Reading, MA: Addison-Wesley.

Tellis, G. J. (2004). Effective advertising: How, when,and why advertising works. Thousand Oaks,CA: Sage.

Tellis, G. J., Chandy, R., & Thaivanich, P. (2000).Decomposing the effects of direct advertising:Which brand works, when, where, and how long?Journal of Marketing Research, 37, 32–46.

Tellis, G. J., & Franses, P. H. (in press). The optimaldata interval for econometric models of advertis-ing. Marketing Science.

Tellis, G. J., & Weiss, D. (1995). Does TV advertis-ing really affect sales? Journal of Advertising,24(3), 1–12.

Tellis, G. J., & Zufryden, F. (1995). Cracking theretailer’s decision problem: Which brand to dis-count, how much, when and why? MarketingScience, 14(3), 271–299.

Winer, R. (1986). A reference price model fordemand of frequently purchased goods. Journalof Consumer Research, 13, 250–256.



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