Market Share Models as Approximators of Aggregated Heterogeneous Brand Choice Behavior

The commonly used market share models are all based on the implicit assumption of a homogeneous population. However, studies of individual brand choice behavior tend to reject this basic premise. In this paper we attempt to explain why market share models perform well in spite of this underlying misspecification. A model which describes the individual's brand choice behavior is presented. This model allows an individual to follow either the Bernoulli, Markov or Linear Learning process as well as have different parameters from other people following the same process. A market share model which takes full account of this heterogeneity is derived and is compared to the traditional market share model in which homogeneous of consumers is assumed. The error in prediction which would result from the use of the homogeneous model is specified and its properties are examined. Conditions for the use, of the gravitational-type market share model, and, the first order lagged market share model are provided. It is shown that the homogeneous market share model will do well in time-series estimation but that the results will not always be appropriate for use in managerial decisions regarding forecasting and optimization.