Characterizing Markov-Switching Rational Expectations Models

Markov-switching rational expectations (MSRE) models can yield fresh insights beyond what linear rational expectations (LRE) models have done for macroeconomics, as Davig and Leeper (2007) and Farmer, Waggoner and Zha (2009), among others, have noted and predicted. A lack of tractable methodological foundations, however, may have hindered researchers from uncovering the salient features of MSRE models. This study improves the status quo to a level at which MSRE models can be analyzed as easily and comprehensively as LRE models. Specifically, we provide the conditions for determinacy and indeterminacy in the mean-square stability sense as well as a solution method to general MSRE models. These tasks are accomplished by applying the standard forward method without reference to the eigensystem of a MSRE model, which is unknown due to its inherent nonlinearity. We apply our methodology to a New-Keynesian model subject to regime-switching in monetary policy and find some unforeseen but intuitive determinacy results. Markov-switching in the private sector is also shown to deliver potentially rich dynamics