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 (1993) 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. JEL classification: C13; C22 Key Words: Cointegration; dynamic ordinary least squares estimator; Granger causality Hayakawa is a JSPS research fellow and acknowledges its financial support. Kurozumi's research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology under Grants-in-Aid No. 17203016 and 18730142. 1