A study of bias and systematic change in nonlinear estimation of Bass model parameters

In a highly cited paper Van den Bulte and Lilien (1997) concluded that nonlinear least squares (NLS) estimates of the Bass (1969) model coefficients are substantially biased in situations consistent with many marketing applications and that the parameter estimates change systematically as one extends the number of observations past the peak in the analysis. They concluded that these results make applications of the Bass model "problematic." We will demonstrate here that these conclusions are not warranted. The conclusion that there is systematic change in parameter estimates is based on improper pooling of data and the conclusion that parameter estimates are substantially biased is not supported by the empirical data used by Van den Bulte and Lilien or by proper simulation of the data generation process. We also show through the use of Box's (1971) bias approximation that the bias in typical cases of diffusion data is small and possibly even trivial and that even for the noisy diffusion data employed by Van den Bulte and Lilien the bias in parameter estimates is much smaller than they claim. Contrary to the claim of Van den Bulte and Lilien NLS estimates of the Bass model when the data extend past the peak do not exhibit large biases and are adequate for forecasting applications when used with the "guessing by analogy" method.