  Vector autoregression is an essential tool in empirical macroeconomics and
finance for understanding the dynamic interdependencies among multivariate time
series. In this study, we expand the scope of vector autoregression by
incorporating a multivariate distributional regression framework and
introducing a distributional impulse response function, providing a
comprehensive view of dynamic heterogeneity. We propose a straightforward yet
flexible estimation method and establish its asymptotic properties under weak
dependence assumptions. Our empirical analysis examines the conditional joint
distribution of GDP growth and financial conditions in the United States, with
a focus on the global financial crisis. Our results show that tight financial
conditions lead to a multimodal conditional joint distribution of GDP growth
and financial conditions, and easing financial conditions significantly impacts
long-term GDP growth, while improving the GDP growth during the global
financial crisis has limited effects on financial conditions.
