We consider non-parametric indirect transfer function estimates for plants in closed, loop. Such estimates are derived from the corresponding closed loop system transfer function estimate and knowledge of the controller. In particular, we give expressions for the bias of such estimates. We consider the application of the results to the spectral and empirical transfer function estimates under the assumption of Gaussian noise. In these cases, the bias can be expressed in terms of the experiment time, controller gain and the levels of disturbance and noise. We also briefly consider corresponding expressions for the variance.