Demographic effects and user costs in demand systems have usually been modelled explicitly. A more robust approach is a state space formulation of the demand system, where time-varying intercepts account for the effects of unobservable variables. The author embeds such a system in a vector autoregressive distributed lag model, with a Bayesian hierarchical prior. The model is estimated by a Markov chain Monte Carlo method on samples involving quarterly US and UK data. In the US case, the results are compared with a previously published cointegration analysis of the same data.