One of the benefits of the Engle and Granger (1987) two-step procedure for modelling the relationship between cointegrated variables is that the 'long-run equilibrium' relationship can be estimated consistently by a straightforward OLS regression involving the levels of the variables. Test statistics with appropriate asymptotic distributions can also be computed fairly easily by applying the modifications of Park and Philips (1988). However, the omission of dynamics may well be detrimental to the performance of the estimator in finite samples. In this paper we use a Monte Carlo study to compare various estimators of the long-run parameters. It is found that estimates which include the dynamics are much more reliable, even if the dynamic structure is overspecified. Furthermore, even though t-statistics based on Park and Phillips' fully modified estimator are asymptotically valid, they do not have good finite sample properties. In contrast, the sizes of t-tests based on an estimator which does make use of dynamics are very reliable.