Moments, shocks and spillovers in Markov-switching VAR models

To investigate how economies, financial markets or institutions can deal with stress, we often analyze the effects of shocks conditional on being in a recession or a bear market. MSVAR models are perfectly suited for such analyses because they combine gradual movements with sudden regime switches. In this paper, we develop a comprehensive methodology to conduct these analyses. We derive first and second moments conditional only on the regime distribution and propose impulse response functions for both moments. By formulating the MSVAR as an extended linear non-Gaussian VAR, all results are available in closed-form. We illustrate our methods with an application to stock and bond return predictability. We show how forecasts of means, volatilities and (auto-)correlations depend on the regimes. The effect of shocks becomes highly nonlinear, and they propagate via different channels. During bear markets, shocks have stronger effects on means and volatilities and die out more slowly.