A New Multivariate Product Growth Model

Abstract

To examine cross-country diffusion of new products, marketing researchers have to rely on a multivariate product growth model. We put forward such a model, and show that it is a natural extension of the original Bass (1969) model. We contrast our model with currently in use multivariate models and we show that inference is much easier and interpretation is straightforward. Especially if the number of countries is larger than two. In fact, parameter estimation can be done using standard commercially available software.We illustrate the benefits of our model relative to other models in simulation experiments.These experiments show that in the competing models the cross-country effects are actually very difficult to identify from the data. An application to a three-country CD sales series shows the merits of our model in practice.

Søren Johansen and Katarina Juselius: A Bibliometric Analysis of Citations through Multivariate Bass Models

“…To model the data, we resorted to an innovative dynamic multivariate versionproposed in Boswijk et al (2009)-of the well-known Bass (1969) model. It was a pleasure for us to observe and emphasize that this model resembles so closely the Vector ECM model popularized by KJ and SJ; in particular, the bilinear nature of the model allows to use the Hansen (2003) algorithm to maximize the likelihood, which generalizes Johansen's ML algorithm, adapting it to a rather general class of restrictions, which includes our case.…”

“…Interestingly, the dynamic pattern of the two indices is quite different: the citation peak in the applied literature does not seem to be reached yet, whereas the peak in the methodological literature seems to have occurred around the turn of the century. To analyze these bibliometric data, we resorted to a multivariate dynamic version of the well known Bass (1969) model, proposed by Boswijk et al (2009) building on Franses (2003), Boswijk and Franses (2005) and Fok and Franses (2007). Bibliometric evidence suggests that Bass-type models provide a useful way to fit most Nobel in Economics prize winner citation trajectories; see Bjork et al (2014).…”

“…In other words, if the observed time span includes the inflection point and the sampling frequency is reasonably high, their results suggest that using the standard normal and the χ 2 for making inference on the parameters is a reasonable approximation. Boswijk et al (2009), henceforth BFF, propose a multivariate generalization of ( 19). The BFF model is made up of n equations, and can be written as follows:…”

“…13 Actually, Boswijk et al (2009) propose an heteroskedastic version of the model, where u t = diag c φ i,t−1 ε t , with ε t = [ε 1,t , ..., ε n,t ] ∼ iidN n (0, Ω ε ) and φ fixed to either 1/2 or 1. In this paper we only briefly discuss the heteroskedastic BFF model, since in our application suitable heteroskedasticity tests seem to accept the hypothesis of homoskedasticity.…”

Knowledge Diffusion and Knowledge Transfer: Two Sides of the Medal

“…I follow Boswijk and Franses (2005) and Boswijk et al (2006) who derived a stochastic counterpart of the Bass (1969) model by assuming short-run deviations from the deterministic diffusion process in a one-dimensional model. To arrive at our stochastic counterpart of system (11) it has to pointed out first that the cumulative numbers of innovators 13 and imitators are both random variables with…”