Determinacy and Classification of Markov-Switching Rational Expectations Models

Abstract

In a general class of Markov-switching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Classification of the models into these three mutually disjoint and exhaustive subsets is completely characterized by the most stable solution in the mean-square stability sense. The rationale behind this result comes from the novel finding that the most stable solution plays the same role as what the generalized eigenvalues do for linear rational expectations models. Moreover, the solution has its own identification condition that does not require examining the entire solution space. The accompanying solution procedure is therefore computationally efficient, and as tractable as standard solution methodologies for linear rational expectations models. The proposed methodology unveils several important implications for determinacy in the regime-switching framework that differ from the linear model counterpart.