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First purchase diffusion model

The seminal first purchase model is the Bass (1969) model of the timing of first purchase of new products, especially consumer durables. The Bass model is based on the assumption that the timing of a consumer’s initial purchase of a new product is related to the number of its previous buyers. The behavioral rationale for the model is rooted in two types of customer behavior: innovative and imitative.

The model is given by

St = (a + bCSt)(M − CSt) + εt (1)

where St is first purchases of a product category at time t, CSt is the cumulative first purchases of the product category at the beginning of t,a and b are parameters representing the coefficients of external influence (innovation) and internal influence (imitation or word of mouth), M is the product category’s market potential parameter, and ε is an error term. Bass empirically tested the model using data from 11 consumer durables.

The model predicts the sales peak and the timing of peak well on these historical data. Several models have tested or applied the Bass model. For example, Dodds (1973) tested long-term sales forecasts of cable television from the Bass model using data from Television Digest during 1963–1966. He found that the Bass model offered a very good description of the adoption pattern for cable television. Tigert and Farivar (1981) assessed the performance of the Bass model using quarterly and annual sales data.

In particular, they addressed the question of how many monthly or quarterly periods are required for the diffusion model to show stability and robustness for data on scanning equipment. They found that the Bass model and a modified analog of the Bass model produced robust results in the estimation period. However, the models failed to predict sales levels accurately in subsequent time periods.

They concluded that no forecasting model should be a substitute for other elements in the strategic planning process and that an in-depth analysis of 3Most models in the literature have been developed for goods, not services. Although many factors that drive the adoption and success of service innovations are the same as those for goods, some are unique to services (see Berry et al., 2005 for a detailed review).

62 VENKATESH SHANKAR product/market structure is required to justify the choices relating to the adopting unit, initial estimates of market potential, level of temporal aggregation of the data, and the starting period for the analysis. Mahajan, Muller, and Srivastava (1990) use the Bass model to develop adopter categories for a product innovation.

By estimating the Bass model over data on 11 consumer durable products, they found that their diffusion model of adopter classification has several advantages over the classical categorization scheme of Rogers:

◆ It yields a category structure in which the size of adopter categories is not assumed to be identical for all innovations.

◆ Interstudy comparisons across the various products can be based on the basic parameters of the diffusion models.

◆ Unlike Rogers’ classification, it does not assume a normal distribution for adoptors. Easingwood, Mahajan, and Muller (1983) extend the Bass model through a Nonuniform Influence (NUI) diffusion model, which relaxes three assumptions of the Bass model:

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