A Unified Approach to Determinacy Conditions with Regime Switching

The conditions that ensure the existence of a unique stable equilibrium – determinacy conditions - for rational expectations models with Markov switching depend on the stability concept, contrasting with standard linear rational expectations models. In this paper, we offer a unified framework for the two commonly used stability concepts (boundedness and mean-square stability) and derive determinacy conditions based on simple metrics. We especially show that, qualitatively, mean-square stable solutions are always at least as many as bounded solutions: no mean-square stable solution implies no bounded solution, a unique mean-square stable solution implies either a unique or no bounded solution, and a model with multiple mean-square solutions can have multiple, unique or no bounded solution. We then provide for two economic applications and show that, in these examples, the determinacy frontiers for the two stability concepts do not perfectly coincide but the difference appears only marginal economically