We propose a new empirical representation of the Bass diffusion model, in order to estimate the
three key parameters, concerning innovation, imitation and maturity. The representation is
based on the notion that the observed data may temporarily deviate from the mean path
determined by the underlying hazard rate. Additionally, it rests on the idea that uncertainty
about the cumulative process should be smaller, the closer it is to the start of the process and to
the level of maturity. Taking this into account, we arrive at an extension of the basic
representation proposed in Bass (1969), with an additional heteroskedastic error term. The type
of heteroskedasticity can be set by the modeler, as long as it obeys certain properties. Next, we
discuss the asymptotic theory for this new empirical model, that is, we focus on the properties of
the estimators of the various parameters. We show that the parameters, upon standardization
by their standard errors, do not have the conventional asymptotic behavior. For practical
purposes, it means that the t-statistics do not have an (approximate) t-distribution. Using
simulation experiments, we address the issue how these findings carry over to practical
situations. In a next set of simulation experiments, we compare the new representation with
that of Bass (1969) and Srinivasan and Mason (1986). We document that these last two
approaches often seriously overestimate the precision of the parameter estimators. We also
shed light on the effects of temporal aggregation and on the effects of a serious and persisent
deviation between the actual data and their mean. Finally, we consider the various empirical
representations for a monthly series on installed ATMs
