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.