Data-based priors for vector error correction models

We propose two data-based priors for vector error correction models. Both priors lead to highly automatic approaches which require only minimal user input. For the first one, we propose a reduced rank prior which encourages shrinkage towards a low-rank, row-sparse, and column-sparse long-run matrix. For the second one, we propose the use of the horseshoe prior, which shrinks all elements of the long-run matrix towards zero. Two empirical investigations reveal that Bayesian vector error correction (BVEC) models equipped with our proposed priors scale well to higher dimensions and forecast well. In comparison to VARs in first differences, they are able to exploit the information in the level variables. This turns out to be relevant to improve the forecasts for some macroeconomic variables. A simulation study shows that the BVEC with data-based priors possesses good frequentist estimation properties.