A new criterion for estimating the order of an ARX model is presented. The proposed criterion is defined for replacing the LS loss function in traditional criteria for model order selection by an estimate of the noiseless value of the LS loss function, The estimate is computed by means of the instrumental variable technique. The consistency of the estimate is proved for a relatively general condition upon the noise : the transfer function of the noise may be time-varying and of infinite order. The relation with the rank test is shown. Simulation results are included for illustration.