Moments, shocks and spillovers in Markov switching VAR models

To investigate how economies, financial markets or institutions can deal with stress, we nowadays often analyze the effects of shocks conditional on a recession or a bear market. MSVAR models are ideally suited for such analyses because they combine gradual movement with sudden switches. In this paper, we develop a comprehensive framework with methods to conduct these analyses. We first derive first and second moments conditional on only a set of regime probabilities. Next, we propose generalized impulse response functions of first and second moments to shocks originating from the regime process, the structural innovations and the variables themselves. By formulating the MSVAR as an extended linear non-Gaussian VAR for the combination of the regime process and the level and squares of the observable variables, all results are in closed-form, which eases a detailed investigation. We illustrate our methods with an application to stock and bond return predictability. Our results show how regime switching combined with predictor variables influences means, volatilities and (auto-)correlations. The impulse response functions show that the effect of shocks becomes highly nonlinear, and that they propagate via different channels. During bear markets, shocks have stronger effects on means and volatilities and die out more slowly.