Parameter variation and new product diffusion

Abstract

In this paper, an empirical investigation into parameter variation in diffusion models is conducted. Specifically, parameter estimates for two consumer durable products are obtained for time-invariant, flexible-form and stochastic-parameter specifications. Existing diffusion models considered in the empirical analysis include the Bass (1969), Easingwood, Mahajan and Muller (1983), Kamakura and Balasubramanian (1987) and Horsky (1990) diffusion models. In addition, a new model is developed that can be estimated with varying parameter structures, and which includes marketing-mix variables and replacement sales. In the empirical analysis, three estimation procedures are employed: non-linear least squares, a stationary stochastic procedure (Harvey and Phillips' 1982 ‘Return to Normality’ model using the Kalman filter), and a non-stationary stochastic specification (Cooley and Prescott, 1973, 1976). The results suggest that stochastic parameter specifications can be easily used to produce substantially better fits and that the improvement can be dramatic. Stochastic parameter specifications are especially useful in the case of weak priors on the likely pattern of variation. Since some degree of parameter variation is often likely to exist, specifying the exact form of the variation is important, albeit difficult. Stochastic parameter specifications can be very helpful in this regard. In addition, tracing the parameter path over time can assist in detecting how current period parameter estimates deviate from the average over this life of the sample. © 1998 John Wiley & Sons, Ltd.