Abstract
In this chapter, models will be classified according to three distinguishable purposes or intended uses, namely:
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1.
descriptive models whose intention it is to describe decision processes;1
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2.
predictive models aiming at forecasting or prediction of future events;
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3.
normative models on the basis of which recommended or optimal courses of action can be determined.
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References
As indicated in Chapter 4, descriptive models of other processes, such as stochastic brand choice, are examined in Chapter 10.
The nature of the decision (structured versus unstructured) and its relation to where in the organization we are most likely to find models is discussed in Chapter 13.
Some symbols have been adopted to be consistent with our notation.
The full procedure related to a price decrease can be deduced from Figure 7.1, in analogy to that following a price increase.
This is a test of the accuracy of the model’s output. Howard and Morgenroth also present a test of the process, i.e. does the model describe the process used by the manager to come to his decision.
Note that markup is defined here as a percentage of price and not of cost.
As such, the model is an illustration of side benefit 8 from Section 3.2.
This study can be considered an example of model building to advance knowledge of marketing phenomena (Section 3.3).
The figures in parentheses are the estimated standard errors of the corresponding estimated parameters.
Other specifications including, for example, lagged market share were also estimated by Leeflang. We keep to (7.1) for simplicity of the argument, not because of its realism.
All data are bimonthly, except for total advertising expenditures.
B.B.C. stands for Bureau voor Budgetten-Controle.
A simple arithmetic average, i.e., without adjustment for sales volume.
It should be clear, however, that to fully exploit the example, one should be able to assess the impact on product class sales of a change in price or advertising of brand j on Q t .This, of course, requires the use of the product class equation, and not one expected value. This is shown in relation (8.5).
Where 0.862 = 1/(1 + 0.16), representing a sales tax of 16 per cent.
Variable cost per unit is assumed to be constant. Given the range limits we imposed, the assumption will be reasonable.
The statistical quality of the results as measured by t-statistics, and R 2 was quite high. 18. As shown in Section 5.3.2.2, this results from assuming a geometrically decaying lag structure, with an identical lag parameter for each of the explanatory variables, a hardly tenable proposition. In addition, the data base consisted of yearly data. Following the discussion in Section 5.3.2.1, a data interval bias is likely to be present, and extreme care should therefore be taken in the interpretation of the results.
Given the footnote related to the assumed lag structure (18), there will not only be substantial variance in the estimated parameters, but the estimates themselves could be biased, i.e. their expected values might differ from the true parameter values. One cannot expect a model to be better than its estimates.
We should, nevertheless, be aware that most other objectives, such as short term sales maximization and growth maximization are consistent with an overall objective of long term profit maximization.
Given a specific campaign, with a specific copy and media plan, this should allow us to make an appropriate adjustment of the advertising parameter. This way of combining data-based parameterization with subjective parameterization was first suggested by Lambin (1972b), and will be elaborated upon in Chapter 11. This point also relates to the issue of a hierarchy of models, and will as such be dealt with again in Chapter 13. See also Leeflang (1977b, 1977c), Reuyl (1977).
This is not given in Lambin’s (1969) paper but can be derived from data in the article as shown in Naert (1973). The fact that the constant term is negative need not trouble us here, as will appear from subsequent discussion. It relates to robustness having to be looked upon from the point of view of intended model use.
Except of course that, taking fixed costs into account, the company may decide to go out of business.
Following the Dorfman-Steiner (1954) theorem derived in the Appendix to this chapter.
Since in (7.13) sales is only a function of advertising, we could write dq/da. We continue to write ∂q/∂a to remind us that (7.13) was itself derived from a demand function where other explanatory variables had been incorporated.
This rather complicated-looking way of writing results from the fact that in equation (7.12) logarithms to the base ten were used, and not natural logarithms.
Or at least, the demand equation did not take into account any element of competitive rivalry, i.e. a monopoly was assumed. Also the Dorfman-Steiner theorem was derived for a monopoly. An extension to oligopolistic markets was provided by Lambin, Naert and Bultez (1975), and will be.touched upon in Chapter 8.
The budget itself could have been determined from an optimization model operating at a more aggregate model, such as the one discussed in Section 7.3.1. It is also conceivable, of course, to have both budget determination and allocation in one single model.
In general multiproduct phenomena, in terms of optimization and allocation, are quite difficult to model, especially when implementation is our main concern, and when reliable parameter estimates are needed. For an elaborate study of the multiproduct problem, we refer to Bultez (1975).
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© 1978 H. E. Stenfert Kroese B. V.
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Naert, P.A., Leeflang, P.S.H. (1978). Specifying models according to intended use. In: Building Implementable Marketing Models. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6586-4_7
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DOI: https://doi.org/10.1007/978-1-4615-6586-4_7
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