State-Dependent Probability Distributions in Non Linear Rational Expectations Models

In this paper, we solve a large class of non-linear rational expectations models with regime switching, i.e. recurring shifts in parameters. The regime-switches and the shocks may follow state-dependent probability distributions. Using a perturbation approach, we first prove that sufficient conditions ensuring the existence of a unique stable equilibrium follow from the corresponding conditions in a regime-switching model with state-independent probabilities. Second, we provide first and second order Taylor expansions of the solution in subclasses of models. Third, we show that state-dependence modifies solution at first-order if the steady-state differs across regimes, otherwise, it only modifies higher orders. Finally, we illustrate our results with a Fisherian model of inflation determination and a New-Keynesian model in which monetary policy switches endogenously between a less-active (dovish) and a more-active (hawkish) reaction against inflation. These examples highlight that the state-dependent fluctuations of transition probabilities can substantially alter the equilibrium dynamics through economic agents' expectations.