E-stability vis-a-vis Determinacy in Regime-Switching Models

This paper examines E-stability, determinacy, and indeterminacy in a general class of regime-switching models with lagged endogenous variables. Using determinacy conditions from Cho (2016, 2020), our first result extends McCallum (2007) to models with time-varying parameters: the unique mean-square stable equilibrium is E-stable if agents have current information and one-period-ahead decision rules. Further, we address the existence of E-stable non-fundamental equilibria, and find that Iteratively E-stable equilibria of indeterminate switching models can exist. Finally, we show that indeterminate New Keynesian models with persistent, recurring interest rate peg regimes admit Iteratively E-stable equilibria. In special cases, the Iterative E-stability condition coincides with the Long Run Taylor Principle.