This paper provides an empirical Bayesian approach to the problem of jointly estimating the lag order and the cointegrating rank of a partially non-stationary reduced rank regression. The method employed is a variant of the Posterior Information Criterion (PIC) of Phillips and Ploberger (1994, 1995) and is similar to the asymptotic predictive odds version of the PIC criterion given in Phillips (1994). Here, we use a proper (Gaussian) prior whose hyperparameters are estimated from an initial subsample of the data.