A bias-correction method for closed-loop identification, introduced in the literature as the bias-eliminated least-squares (BELS) method (Zheng & Feng,Automatica 31 (1995) 1019), is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed-loop system. This predictor is a function of the plant parameters and the known controller. Corresponding to the related method using a least-squares criterion, the method is referred to as the tailor-made IV method for closed-loop identification. The indicated equivalence greatly facilitates the understanding and the analysis of the BELS method.