Modelling errors are often the limiting factor in identification problems. Therefore, it is important to qualify their impact on the estimated plant model parameters. This paper qualifies the influence of model errors and disturbing noise level on (i) the asymptotic value (estimate for an infinite amount of data), and (ii) the asymptotic (amount of data going to infinity) covariance matrix of the estimated model parameters. The theory is elaborated on a time domain and a frequency domain estimator.