A model of multiple-unit ownership as a diffusion process

This paper develops and tests a new model for multiple-unit adoptions of durable goods based on the diffusion modeling tradition. Multiple-unit adoptions are a major component of sales for many consumer durable product categories. For instance, sales of multiple-unit adoptions for televisions have been higher than both first adoptions and replacement purchases since 1977, while for automobiles, they have represented more than 20% of sales since 1966 in Australia. The structural drivers of multiple-unit adoptions are quite different from either first purchase or replacement purchase. Hence, identifying and modeling the multiple-unit component of sales is important for aggregate sales forecasts. Moreover, consumer requirements for additional units of a product are likely to be considerably different than for the other components of sales (first purchases and replacement purchases). As such, the ratio of the first, multiple, and replacement sales components will strongly influence the product mix requirements of the market.

While forecasting and influencing multiple-unit sales are an important managerial issue, very little attention has been given to multiple-unit ownership in the diffusion modeling literature. The only model available was developed for the purpose of modeling relatively short-term behavior of multiple-unit adoptions, rather than the longer-term pattern of sales. We propose a model of multiple-unit adoptions as a diffusion process.

We apply the model to both color television and automobiles. Analysis of the model's long-term fit and forecasts in these applications provide support for the structure of the new model.