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This paper develops methods for automatic selection of variables in forecasting Bayesian Vector AutoRegressions (VARs) using the Gibbs sampler. In particular, the author provides computationally efficient algorithms for stochastic variable selection in generic (linear and nonlinear) VARs. The performance of the proposed variable selection method is assessed in a small Monte Carlo experiment, and in forecasting 4 macroeconomic series of the UK using Time-Varying Parameters Vector AutoRegressions (TVP-VARs). Restricted models consistently improve upon their unrestricted counterparts in forecasting, showing the merits of variable selection in selecting parsimonious models.
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