We study the consequences of using a deterministic steady state in Vector Autoregressive (VAR) models, when the data may display structural breaks, transitional dynamics or low-frequency fluctuations. We document upward biases in the estimated coefficients. Distortions are amplified by the identification scheme. Allowing the steady state to be stochastic reduces the biases. We propose a spike-and-slab prior to differentiate between the two alternative long-run specifications. We revisit two