Many economic applications call for simultaneous equations VAR modeling.
We show that the existing importance sampler can be prohibitively inefficient for this type of models. We develop a Gibbs simulator that works for both simultaneous and recursive VAR models with a much broader range of linear restrictions than those in the existing literature. We show that the required computation is of an SUR type, and thus our method can be implemented cheaply even for large systems of multiple equations. The authors have benefited from discussions with John Geweke and Chris Sims. The code for computation is available upon request.