It has been argued that the frequency domain accuracy of high
model-order estimates obtained on the basis of closed loop data is
largely invariant to whether direct or indirect approaches are used.
The analysis underlying this conclusion has employed variance
expressions that are asymptotic both in the data length and
the model order, and hence are approximations when either of these
are finite. However, recent work has provided variance expressions
that are exact for finite (possibly low) model order, and
hence can potentially deliver more accurate quantification of
estimation accuracy. This paper revisits the study of
identification from closed loop data in light of these new
quantifications and establishes that, under certain assumptions of white
spectra, there can be significant differences in the accuracy
of frequency response estimates that are dependent on what type of
direct, indirect or joint input-output identification strategy is
pursued.