Gaussian and Student's $t$ mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area

A new mixture vector autoregressive model based on Gaussian and Student's $t$ distributions is introduced. As its mixture components, our model incorporates conditionally homoskedastic linear Gaussian vector autoregressions and conditionally heteroskedastic linear Student's $t$ vector autoregressions. For a $p$th order model, the mixing weights depend on the full distribution of the preceding $p$ observations, which leads to attractive theoretical properties such as ergodicity and full knowledge of the stationary distribution of $p+1$ consecutive observations. A structural version of the model with statistically identified shocks and a time-varying impact matrix is also proposed. The empirical application studies asymmetries in the effects of the Euro area monetary policy shock. Our model identifies two regimes: a high-growth regime that is characterized by positive output gap and mainly prevailing before the Financial crisis, and a low-growth regime that characterized by negative but volatile output gap and mainly prevailing after the Financial crisis. The average inflationary effects of the monetary policy shock are stronger in the high-growth regime than in the low-growth regime. On average, the effects of an expansionary shock are less enduring than of a contractionary shock. The CRAN distributed R package gmvarkit accompanies the paper.