Abstract
In Section 4.2, we suggested distinguishing three classes of market demand functions, namely product class sales, brand sales, and market share models.1 As was indicated there, such a classification may be useful because model specification — both in terms of variables and mathematical form — will show some distinctive features relative to each of thesethree categories.
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References
The literature contains a number of synonyms for product class sales, such as primary demand (see, for example, Leeflang 1977a), industry sales or demand (see, for example, Lambin, Naert, Bultez, 1975), and generic demand (Hughes, 1973, p. 2). In analogy to product class sales being called primary demand, brand sales is also referred to as secondary demand.
The observations may also consist of a combination, or — as it is generally referred to in the literature — a pooling of cross section and time series data. Pooling calls for special estimation procedures. A classic example is the estimation of the demand for natural gas by Balestra and Nerlove (1966).
One should not, however, conclude that marketing instruments can never be explanatory variables in cross section models. For example, advertising expenditures cannot be split up across individual consumers, i.e., a firm cannot say that one individual got two dollars worth of advertising, and another person one dollar and fifty cents. But a proxy measure can be obtained by a measure of an individual consumer’s brand awareness.
For similar studies, see Van der Zwan (1968).
It should be observed that having zero-one dependent variables makes one of the basic assumptions of linear regression analysis untenable. See, for example, Goldberger’s discussion on qualitative dependent variables (1964, pp. 248–251).
Another possible specification could have been not to include PI t directly, but to express private disposable income in real terms by dividing y t by PI t For an example, see equation (8.5).
For the other variables we refer to the legend following equation (8.2).
A market share demand function for the same market was given in Section 7.2.
The assumption being that such variables affect demand for each brand equally. This assumption will often be quite reasonable. If not, however, environmental variables affecting brands differently should be included in the market share function, or else one has to resort to direct estimation of brand sales.
This is emphasized by, for example, MacLachlan (1972, p. 378) and Beckwith (1972, p. 171).
After careful reading of Sections 5.3, and Sections 6.3 to 6.5, the reader should be able to evaluate the qualities and deficiencies of this specification.
One, for example, makes a distinction between theories in which one pays specific attention to leaders (Stackelberg) and theories which concentrate on followers (Cournot). See Henderson and Quandt (1971).
In normative marketing mix studies one generally looks for the optimal policy for one brand assuniing particular reaction patterns of competition. This means that, one does not derive a simultaneous optimum for all brands in the product class. The latter would call for a game theoretic approach. Many authors have applied such an approach to a marketing context. Examples are, Friedman (1958), Mills (1961), Shakun (1966), Baligh and Richartz (1967), Gupta and Krishnan (1967a, 1967b), Krishnan and Gupta (1967), Naert (1971). In a dynamic situation, the theory of differential games also seems promising, as was demonstrated by Deal (1975). Most of these models being theoretical and not yet empirical, we will not give them further attention.
The relation thus established is independent of any normative considerations, it does not depend on an assumption of profit maximization or on any other specific objective function.
For a more formal treatment extending to other variables as well, see Lambin, Naert, Bultez (1975, pp. 106–115). In the paper the special character of quality as a decision variable is also discussed. A generalization to multiproduct markets is given by Bultez (1975).
The time and brand index are left out for notational convenience.
The assumptions on competitive behaviour are in many cases implicit rather than explicit.
Here translated into our notation.
When competitive reaction is explicitly taken into account by a firm, it is called a leader in micro-economic jargon.
These and other examples are classified in a systematic fashion in the Lambin, Naert and Bultez article. For a large number of empirical illustrations, see Lambin (1976).
For details on the statistical qualities of these estimates, see Section 6.3, Table 6.1.
In fact some of the variables were introduced in the reaction functions with a one period lag. We will not go into this here.
The figures in brackets are t-statistics. The results provide empirical evidence for the existence of multiple competitive reaction, since differs significantly from zero at the 1% significance level.
As indicated in Section 6.3 this does not make such models useless, but satisfying range and sum constraints are characteristics which are a priori desirable.
There are, of course, other ways of avoiding the aggregation issue. Beckwith (1972), for example, simultaneously estimated a set of linear market share equations, i.e. one for each brand. In estimating the parameters, he exploited the fact that if one or more market shares are higher than expected, this necessarily goes at the expense of some other brands’ shares. This knowledge led Beckwith to apply Zellner’s (1962) method of estimating seemingly unrelated regressions.
For an impressive empirical study of the more classic market share response functions, we refer to Lambin (1976). His data base contained observations in nine countries of Western Europe, covering sixteen product classes, one hundred and seven brands, and extending over a ten year time period. See also Leeflang (1977d, 1978).
There could also be other determining variables, such as, disposable income.
The problem of asymmetry and nonlinearities in relation to the Bell-Keeney-Little theorem has been examined at length by Barnett (1976). His elaboration of the theorem is based primarily on his finding that axiom (3) is not essential to their result.
Nakanashi studied the market share of different brands in different supermarkets. As such his model looked somewhat more complicated than (8.29). Market share becomes m rjt , i.e. market share of brand j in store r in period t, I jit becomes I rjt , and α rj replaces α j Conceptually, however, there is no difference since the response parameters remain ß i
Nakanishi’s transformation is discussed in Section 11.2.
See for example, Snedecor and Cochran (1967, p. 329), or Houston and Weiss (1974, p. 153.)
In fact Nakanishi applies this transformation to all variables; exp(a jt ) stands for
On the meaning of generalized least squares, see Chapter 11.
McGuire, Weiss and Houston (1974) have worked along similar lines.
Bultez (1975, pp. 216–227, and 1977) examined the relation between these two and other linearization procedures.
The details of the estimation procedure are beyond the level of this book.
See Leeflang (1977d, 1978).
Price and quality were also considered effective marketing instruments. Lack of variation in their observed values made econometric estimation impossible. This again points to a case where econometric and subjective estimation methods could profitably be combined.
An estimator is said to be more efficient than another if it has smaller variance.
This is demonstrated in Bultez and Naert (1975, p. 534).
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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 different levels of demand. In: Building Implementable Marketing Models. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6586-4_8
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