Reduced rank regression has a long tradition as a technique to achieve a parsimonious parameterization in multivariate regression models. Recently this has been applied in the Bayesian VAR framework where the rich parameterization is a common concern in applied work. We advocate a parameterization of the reduced rank VAR which leads to a natural interpretation in terms of a dynamic factor model. Without additional restrictions on the parameters the reduced rank model is unidentified and we consider two identification schemes. The traditional ad-hoc identification with the first rows of one of the reduced rank parameter matrices being the identity matrix and a semi-orthogonal identification originally proposed in the context of cointegrated VAR models with the advantage that it does not depend on the ordering of the variables. Borrowing from the cointegration literature, we propose efficient MCMC algorithms for the evaluation of the posterior distribution given the two identification schemes. The determination of the rank of the reduced rank VAR is an important practical issue and we study the performance of different criteria for determining the rank. Finally, the forecasting performance of the reduced rank VAR model is evaluated in comparison with other popular forecasting models for large data sets.