On Priors on Cointegrating Spaces

The focus of inference in Bayesian cointegration analysis has recently shifted from the cointegrating vectors to the cointegrating space. Two recent papers - Strachan and Inder (2004) and Villani (2004) - present uniform priors for the cointegrating space using different specifications for identification of the cointegrating vectors. This note clarifies the links between these approaches and shows that while the implied priors on the cointegrating space are identical, the posteriors have very different forms and this difference has implications for the inferences that can be obtained and for computational ease. Central to explaining these results is the specification of the adjustment coefficients under different identifying restrictions. The discussion extends to results on the priors in Geweke (1996) and Kleibergen and Paap (2002) and the interpretation of cointegrating vectors with linear identifying restrictions.