In this paper, we consider the role of “leads" of the first difference of integrated variables in the dynamic OLS estimation of cointegrating regression models. Specifically, we investigate Stock and Watson's [J.H. Stock, M.W. Watson's, A simple estimator of cointegrating vectors in higher order integrated systems, Econometrica 61 (1993) 783–820] claim that the role of leads is related to the concept of Granger causality by a Monte Carlo simulation. From the simulation results, we find that the dynamic OLS estimator without leads substantially outperforms that with leads and lags; we therefore recommend testing for Granger non-causality before estimating models.