Within-brand and cross-brand word-of-mouth for sequential multi-innovation diffusions

Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest to involved firms. In homogeneous product categories, the model structure should allow distinguishing between within-brand and cross-brand word-of-mouth effects. In this paper, we propose a model that, besides separating these two imitative sources, also allows for a change in the parameter values of the first entrant as soon as the second one enters the market. We prove that our model has a closed-form solution, allowing parameters to be estimated with sales data. Moreover, we compare our model with other unbalanced models, both from a theoretical point of view and from an empirical one, by assessing their performance on pharmaceutical drug data.