State-Dependent Probability Distributions in Non Linear Rational Expectations Models

Abstract

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. First, we provide sufficient conditions for the existence of a unique stable equilibrium using a perturbation approach.Then, we provide Taylor expansions of the solution in subclasses of models. Finally, we put forward that state-dependent fluctuations of transition probabilities can substantially alter the equilibrium dynamics through economic agents' expectations. We illustrate these modifications in the context of a Fisherian model of inflation and a NewKeynesian model in which monetary policy switches endogenously between a passive and an active reaction to inflation.

On the stability of Calvo-style price-setting behavior

“…See Davig and Leeper (2007) and Barthelemy and Marx (2011). 5 We do not include the recent U.S. data in order to avoid the zero lower bound period.…”

Generalizing the Taylor Principle: New Comment

“…This result is an improvement of Proposition 1 in Barthélemy and Marx (2011) as this result gives necessary and sufficient conditions while Barthélemy and Marx (2011) only give sufficient conditions. Proposition 2.…”

“…We base our proof on the formalism introduced by Woodford (1986) and recently used in Barthélemy and Marx (2011). We show that the model can be reformulated as a functional equation (1 − R)φ = ψ 0 where R is an operator, φ the solution and ψ 0 a function depending on shocks and regimes.…”

“…A similar matrix has already been introduced in Barthélemy and Marx (2011). For any p, an (i, j) element of the matrix S p corresponds to an upper bound of the expected impact (in norm) of the future endogenous variables along trajectories starting from regime i to regime j in p steps weighted by the probability of each trajectory.…”

Efficient Perturbation Methods for Solving Regime-Switching DSGE Models

“…3 This is the approach followed by Barthelemy and Marx (2011), Foerster et al (2013Foerster et al ( , 2014 and in this paper.…”