Efficient posterior simulation in cointegration models with priors on the cointegration space

A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identied choice for these vectors). In this note, we discuss a sensible way of eliciting such a prior. Furthermore, we develop a collapsed Gibbs sampling algorithm to carry out efficient posterior simulation in cointegration models. The computational advantages of our algorithm are most pronounced with our model, since the form of our prior precludes simple posterior simulation using conventional methods (e.g. a Gibbs sampler involves non-standard posterior conditionals). However, the theory we draw upon implies our algorithm will be more efficient even than the posterior simulation methods which are used with identied versions of cointegration models.