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We propose the parametric Dynamic Seemingly Unrelated Regression (DSUR) estimator for simultaneous estimation of multiple cointegrating regressions. DSUR is efficient when the equilibrium errors are correlated across equations and is applicable for panel cointegration estimation in environments where the cross section is small relative to the available time series. We study the asymptotic and small sample properties of the DSUR estimator for both heterogeneous and homogeneous cointegrating vectors. We then apply the method to analyse two long-standing problems in international economics. Our first application revisits the estimation of long-run correlations between national investment and national saving. Our second application revisits the question of whether the forward exchange rate is an unbiased predictor of the future spot rate.