Characterizing Markov-Switching Rational Expectations Models

Markov-switching rational expectations (MSRE) models can bring out fresh insights beyond what linear rational expectations (RE) 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 paper improves the status quo to a level at which MSRE - inherently non-linear - models can be analyzed as easily and comprehensively as linear RE models. Specically, we provide a solution method, determinacy conditions, and an economic solution renement and completely characterize the set of RE equilibria for general MSRE models under determinacy and indeterminacy in the mean-square stability sense. These tasks are accomplished by simply solving a model forward and imposing the no-bubble condition for fundamental solutions. We apply our methodology to a New-Keynesian model subject to regime-switching in monetary policy and nd some unforeseen but intuitive determinacy results. Markov-switching in the private sector is also shown to deliver potentially rich dynamics.