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State-Dependent Probability Distributions in Non Linear Rational Expectations Models

  • Magali Marx

    (Banque de France)

  • Jean Barthelemy

    (Banque de France)

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.

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Paper provided by Society for Economic Dynamics in its series 2013 Meeting Papers with number 576.

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Date of creation: 2013
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Handle: RePEc:red:sed013:576
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