In this paper a parametric framework for estimation and inference in cointegrated panel data models is considered that is based on a cointegrated VAR(p) model. A convenient two-step estimator is suggested where in the first step all individual specific parameters are estimated, whereas in the second step the long-run parameters are estimated from a pooled least-squares regression. The two-step estimator can easily be modified to account for contemporaneously correlated errors, a feature that is often encountered in multi-country studies. Monte Carlo simulations suggest that the two-step estimator and related test procedures outperform semiparametric alternatives such as the FM-OLS approach.