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In this paper I propose a parametric framework for modelling and forecasting macroeconomic tail risk based on stochastic volatility models with Skew-Normal and Skew-t shocks featuring stochastic skewness. The paper develops posterior simulation samplers for Bayesian estimation of both univariate and VAR models of this type. In an application, I use the models to predict downside risk to GDP growth and I show that this approach represents a competitive alternative to quantile regression. Finally, estimating a medium scale VAR on US data I show that time varying skewness is a relevant feature of macroeconomic and financial shocks., Comment: 41 pages,7 figures