Methods for Markov-Switching Models

I develop a toolbox to analyze the statistical properties of multivariate Markov-switching models. I first derive analytical formulas for the evolution of first and second moments, taking into account the possibility of regime changes. The formulas are then used to characterize the evolution of expectations and uncertainty, the propagation of the shocks, the contribution of the shocks to the overall volatility, and the welfare implications of regime changes in general equilibrium models. Then, I show how the results can be used to capture the link between uncertainty and the state of the economy. Finally, I generalize Campbell’s VAR implementation of Campbell and Shiller’s present value decomposition to allow for parameter instability. All results are derived analytically, do not require numerical integration, and are therefore suitable for structural estimation.