The New Keynesian model with stochastically varying policies

The Multiplicative Ergodic Theorem provides a novel general methodology to analyze rational expectations models with stochastically varying coefficients. The approach is applied for the first time to economics and analyzes the canonical New Keynesian model with a Taylor rule which switches randomly between an aggressive and a passive reaction to inflation. The paper delineates the trade-off of the central bank of being passive in some periods and aggressive in others. Moreover, it is shown how this trade-off depends on the stochastic process governing the randomness in the central bank's policy. Finally, explicit solution formulas are derived in the case of determinateness as well as indeterminateness. In doing so the paper considerably extends the current approach.