A Bayesian Approach to Restrictions on the Cointegration Space

Mattias Villani

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.

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