Stochastic Volatility-in-mean VARs with Time-Varying Skewness

Abstract: This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic variables. We provide a Gibbs sampling algorithm for posterior inference and apply the model to quarterly data for the US and the UK. Empirical results show that skewness shocks have economically significant effects on output, inflation and spreads, often exceeding the impact of volatility shocks. In a pseudo-real-time forecasting exercise, the proposed model outperforms existing alternatives in many cases. Moreover, the model produces sharper measures of tail risk, revealing that standard stochastic volatility models tend to overstate uncertainty. These findings highlight the importance of incorporating time-varying skewness for capturing macro-financial risks and improving forecast performance.