On the Econometrics of the Bass Diffusion Model

The parsimonious Bass diffusion model is frequently used to forecast adoptions of new products and to compare the life cycles of specific products across countries. To meet these goals, reliable parameter estimates are needed. We develop the asymptotic theory for the three key parameters in the Bass model. For this purpose, we need to make assumptions about the stochastic error process. On doing so, we arrive at an alternative version of the Bass model than the one usually considered in practice, because our model includes an additional variable and it incorporates heteroscedastic errors. The asymptotic theory entails that the parameters, on 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 of how these findings carry over to practical situations. In a next set of simulation experiments, we compare our representation with that of Bass and Srinivasan and Mason. Among other things, we document that these two approaches seriously overestimate the precision of the parameter estimators, and that some parameters suffer from a substantial bias. An analysis of 12 series concerning compact disc penetration supports these simulation results. We see the same type of bias in parameter estimates, and our model delivers more accurate forecasts.

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