We provide a shrinkage type methodology which allows for simultaneous model selection and estimation of vector error correction models (VECM). Model determination is treated as a joint selection problem of cointegrating rank and autoregressive lags. We show consistency of the selection mechanism by the resulting Lasso-VECM estimator under sparsity in lags and cointegration relations. In contrast to existing two-step approaches based on information criteria, we also derive the asymptotic properties of the final estimator and point to estimation refinements. Moreover, with only linear computational complexity, the procedure remains computationally tractable also for higher dimensions. We demonstrate the effectiveness of the proposed approach by a simulation study and an empirical application to recent CDS data after the financial crisis. Joint with Chong Liang.