An Algorithm for Generalized Impulse-Response Functions in Markov-Switching Structural VAR

We transpose the Generalized Impulse-Response Function (GIRF) developed by Koop et al. (1996) to Markov-Switching structural VARs. As the algorithm displays an exponentially increasing complexity as regards the prediction horizon, we use the collapsing technique to easily obtain simulated trajectories (shocked or not), even for the most general representations. Our approach encompasses the existing IRFs proposed in the literature and is illustrated with an applied example on gross job flows.