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Economists derive the relationships between prices and demands from utility theory which implies that the sensitivity of the demand for brand A to the price of brand B will be the same as the sensitivity of the demand for brand B to the price of brand A. This elementary proposition of the economic theory of demand underlies most econometric procedures for estimating demand relations such as the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980).
Conventional wisdom among marketing professionals is that there is more to demand determination than price and, moreover, that the sensitivities of demands to prices is not symmetric. Furthermore, the necessary presumption of most econometric analysis, including AIDS, that relations are linear and observations are drawn from independent and identically distributed sets of possible observations is more restrictive than is appropriate for application to the rough and ready uses of working marketing professionals.
In this paper, we use both linear and non-linear statistical techniques to identify competitive sets. We eschew the imposition of symmetry on our results so that, for example, a brand with a small market share might see a large-share brand as a strong competitor but the strong brand does not notice the small-share brand. The interpretation and utilisation of the results are driven by a rulebase incorporating the domain expertise of one of us (Sims). The non-linear statistical techniques were developed for this system by Campbell from the local regression algorithms of Cleveland and Devlin(1988). The procedures for guiding the rulebased analysis are closely integrated with the explanatory power of the system as developed by Moss (1995). The whole system was implemented in SDML, a strictly declarative modelling language which runs on top of the VisualWorks development of Smalltalk-80.*1 The advantage of SDML is that it is a proper superset of Konolige's (1992) strongly grounded autoepistemic logic so that the formal properties of the system are known and the generality of results can be proved (or disproved) within the framework of that formal system. The point here is that the results obtained within SDML are as rigorous as those obtained by (say) econometricians and statisticians. Moreover, in some cases, necessary and/or sufficient conditions can be found which demonstrate the generality or lack of generality of results.
The next section describes the determination of competitive sets. Then, in section 3, we consider a pilot case which is nonetheless interesting in its own right. In section 4, we apply the methods to a large data set in which we identify a competitive set of fewer than a dozen brands from a data set covering more than 60 brands over more than three years with weekly EPOS (electronic-point-of-sale) data for each brand. Finally, in section 5, we indicate how this part of the system relates to the whole and how we validate our results by means of simulation experiments and knowledge-based representations of the demand side of the markets for FMCGs. A description of local regression and the particular developments required for application here is contained in the appendix.
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