State-Dependent Probability Distributions in Non Linear Rational Expectations Models

In this paper, we provide solution methods for non-linear rational expectations models in which regime-switching or the shocks themselves may be "endogenous", i.e. follow state-dependent probability distributions. We use the perturbation approach to find determinacy conditions, i.e. conditions for the existence of a unique stable equilibrium. We show that these conditions directly follow from the corresponding conditions in the exogenous regime-switching model. Whereas these conditions are difficult to check in the general case, we provide for easily verifiable and sufficient determinacy conditions and first-order approximation of the solution for purely forward-looking models. Finally, we illustrate our results with a Fisherian model of inflation determination in which the monetary policy rule may change across regimes according to a state-dependent transition probability matrix.