This and a companion paper focus on the accurate quantification of the way noise induced estimation errors are dependent on model structure, underlying system frequency response, measurement noise and input excitation. This study exposes several new principles. In particular, it is shown that when employing Output--Error and Box--Jenkins model structures in a prediction-error framework, then the ensuing estimate variability in the frequency domain depends on the underlying system pole positions. As well, it is also established that the variability is affected by the choice of model structure. For example, with fixed noise model, it is twice as much when system poles are estimated as when they are a-priori known and fixed, even though the model order is the same in both cases. These results, together with others presented here and in a companion paper, are unexpected according to pre-existing theory. They depend on new techniques and results developed by the authors in the area of rational orthonormal bases, with the idea of a `reproducing kernel' playing a key role.