A Bayesian reference analysis of the cointegrated vector
autoregression is presented based on a new prior distribution. Among other
properties, it is shown that this prior distribution distributes its
probability mass uniformly over all cointegration spaces for a given
cointegration rank and is invariant to the choice of normalizing variables
for the cointegration vectors. Several methods for computing the posterior
distribution of the number of cointegrating relations and distribution of
the model parameters for a given number of relations are proposed,
including an efficient Gibbs sampling approach where all inferences are
determined from the same posterior sample. Simulated data are used to
illustrate the procedures and for discussing the well-known issue of local
nonidentification.The author thanks Luc
Bauwens, Anant Kshirsagar, Peter Phillips, Herman van Dijk, four anonymous
referees, and especially Daniel Thorburn for helpful comments. Financial
support from the Swedish Council of Research in Humanities and Social
Sciences (HSFR) grant F0582/1999 and Swedish Research Council
(Vetenskapsrådet) grant 412-2002-1007 is gratefully acknowledged.
The views expressed in this paper are solely the responsibility of the
author and should not be interpreted as reflecting the views of the
Executive Board of Sveriges Riksbank.