Econometric models of advertising

Advertising is a powerful form of marketing communication used to "encourage, persuade, or even manipulate an audience to take or continue to take some action". The final desired result is to drive consumer behavior with respect to a commercial offering, although political and ideological advertising is also common. The marketing mix has been the key concept to advertising. The marketing mix refers to four variables (the 4 P's) that a marketing manager can control in order to influence a brand’s sales or market share. The basic question that managers face nowadays is, what level or combination of these variables maximizes sales, market share, or profit? Or, otherwise, "How do sales or market share respond to past levels of or expenditures on these variables"?

Researchers have developed a variety of econometric models of market response to the marketing mix, most of these which have focused on market response to advertising or pricing (Sethuraman, 1991). The reason may be that expenditures on these variables seem the most discretionary, so marketing managers are most concerned about how they manage these variables. The basic philosophy underlying the approach of response modeling is that past data on consumer and market response to the marketing mix contain valuable information that can enlighten our understanding of response. 

Seven response models to advertising are have been already patternalized: Current, shape, competitive, carryover, dynamic, content and media effects of advertising. The first four are common across price and the other marketing variables. The last three are unique to advertising. 

Current and Carryover Effect

The current effect of advertising is the change in sales caused by an exposure of advertising occurring at the same time period as the exposure. The x-axis here is time, while sales are on the y-axis and the baseline sales are the dashed line. The current effect of advertising is the spike in sales from the baseline given an exposure of advertising. Decades of research indicate that this effect of advertising is small relative to that of other marketing variables and quite fragile, as it can be easily drowned out by the noise in the data. It can be captured by the model:

Yt = a + b1 At + b2Pt + b3Rt + b4Qt +  et 

where Y represents the dependent variable (e.g. sales), while the other capital letters represent variables of the marketing mix, such as advertising (A), price (P), sales promotion (R), or quality (Q). The parameters a and bk are coefficients that the researcher wants to estimate. bk represents the effect of the independent variables on the dependent variable, where the subscript k is an index for the independent variables. et are errors that can be approached as "white noise".

The carryover effect of advertising is that portion of its effect that occurs in time periods following the pulse of advertising. The carryover effect may occur for several reasons, such as delayed exposure to the ad, delayed consumer response, delayed purchase due to consumers’ backup inventory, delayed purchase due to shortage of retail inventory, and purchases from consumers who have heard from those who first saw the ad (word of mouth). The carryover effect may be as large as or larger than the cur-rent effect. Typically, the carryover effect is of short duration, rather than of long duration. It can be captured by the multiplicative model:

Yt = Exp(a) At b1 Pt b2 Rt b3 Qt b4 et

with sales (Y), advertising (A), price (P), sales promotion (R), quality (Q) inter correlated. Here, the independent variables have a synergistic effect on the dependent variable. In many advertising situations, the variables could indeed interact to have such an impact. For example, higher advertising combined with a price decrease may enhance sales more than the sum of higher advertising or the price drop occurring alone.

Shape Effect

The shape of the effect refers to the change in sales in response to increasing intensity of advertising in the same time period. The intensity of advertising could be in the form of exposures per unit time and is also called frequency or weight. The x-axis now is the intensity of advertising in a period, while the y-axis is the response of sales.  It can be captured by the exponential attraction model:

Mi = Exp (Vi )/Σ Exp Vj 

where Mi is the market share of the ith brand (measured from 0 to 1), Vj is the marketing effort of the jth brand in the market, Σ stands for summation over the j brands in the market, Exp stands for exponent, and Vi is the marketing effort of the ith brand. We know that Vi = a + b1 Ai + b2Pi + b3Ri + b4Qi + ei, as aforementioned, thus:

Mi  = Exp (Vi )/Σ Exp Vj = Exp (Σbk  Xk  + e)/ Σj Exp(Σkbk Xik + ej),

where Xk (0 to m) are the m independent variables or elements of the marketing mix, a = b0 and Xi0 = 1. The use of the ratio of exponents in the above equations ensures that market share is an S-shaped function of share of a brand’s marketing effort.

The diagram above shows three typical shapes: linear, concave and S-shape. Of these three shapes, the S-shape seems the most plausible because it suggests that at some very low level, advertising might not be effective at all because it gets drowned out in the noise. At some high level, it might not increase sales (advertising elasticity-->0) because the market is saturated or consumers are insensitive from the repetitive advertising.

Competitive Effect

Advertising normally takes place in free markets. Whenever one brand advertises a successful innovation or successfully uses a new advertising form, other brands quickly imitate it. Competitive advertising tends to increase the noise in the market and thus reduce the effectiveness of any one brand’s advertising. The competitive effect of a target brand’s advertising is its effectiveness relative to that of the other brands in the market.  The simplest method of capturing advertising response in competition is to measure and model sales and advertising of the target brand relative to all other brands in the market with more complex models, mainly based on the aforementioned econometric model of the "Shape Effect". These first four models may also apply to "Price" instead of "Sales" dependent variable.

Dynamic, Contents and Media Effect

Dynamic effects are those effects of advertising that change with time. Included under this term are carryover effects discussed earlier and wearin, wearout effects. Wearin is the increase in the response of sales to advertising, from one week to the next of a campaign, even though advertising occurs at the same level each week. Wearout is the decline in sales response of sales to advertising from week to week of a campaign, even though advertising occurs at the same level each week. Wearout typically occurs at the end of a campaign because of consumer indifference. 

Content effects are the variation in response to advertising due to variation in the content or creative cues of the ad. This is the most important source of variation in advertising responsiveness and the focus of the creative talent in every agency. Thus, the challenge for marketers is to include measures of the content of advertising when modeling advertising response in real markets.

Media effects are the differences in advertising response due to various media, such as TV, or newspaper, and the programs within them, such as channel for TV or section or story for newspaper.

The last three effects (dynamic, content, media) may be captured by models similar to the S-shaped response with modeling interactions integrated due to the competitive environment or even competitive distributed lag Models, however in reality their mathematics can be quite complex (Tellis, 2006).   

Conclusion

Prudent marketing managers need to take into account how markets have responded to the marketing mix in the past. Past may predict future with relative certainty but it also contains valuable lessons that might enlighten the future. The aforementioned econometrics of response modeling describe how a researcher should model response to the marketing mix and especially to advertising in order to capture and control the most important effects validly. Which may be the "raison d'être" for marketing managers, in the first place.

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