Mattias Villani

**Abstract**

The degree of empirical support of a priori plausible structures on
the cointegration vectors has a central role in the analysis of cointegration.
Historically, this question has been answered by testing over-identifying
restrictions on the cointegration space. An intrinsic problem with hypothesis
tests is that the investigator often faces a situation with many a priori
plausible restrictions and it is usually far from clear how to draw conclusions
from a bundle of (dependent) hypothesis tests. Partly as a response to
this, this paper introduces a Bayesian procedure to calculate the posterior
probability of restrictions on the cointegration space, which is valid
for any sample size. Such probabilities are easy to interpret and can be
used in many productive ways, e.g. to weigh the predictions produced from
the different models defined by the restrictions. The procedure is illustrated
on U.S. consumption-income data. A small simulation study suggests that
the proposed Bayesian approach is very promising.

Keywords: Cointegration, Posterior probability, Restrictions.