This paper establishes that when using a least squares criterion to
estimate an output error type model structure, then
the measurement noise induced variability of the frequency response
estimate depends on the estimated (and hence also on the true) pole
positions. This dependence on pole position is perhaps counter to
prevailing wisdom that for any `shift invariant' model structure,
the variability depends only on model order, data length, and input
and noise spectral densities. That is, it is counter to the belief that
variance error is model-structure independent.