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State-Dependent Probability Distributions in Non Linear Rational Expectations Models

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  • Barthélemy, J.
  • Marx, M.

Abstract

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.

Suggested Citation

  • Barthélemy, J. & Marx, M., 2011. "State-Dependent Probability Distributions in Non Linear Rational Expectations Models," Working papers 347, Banque de France.
  • Handle: RePEc:bfr:banfra:347
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    References listed on IDEAS

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    Cited by:

    1. Barthélemy, J. & Marx, M., 2012. "Generalizing the Taylor Principle: New Comment," Working papers 403, Banque de France.
    2. Lhuissier, Stéphane & Zabelina, Margarita, 2015. "On the stability of Calvo-style price-setting behavior," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 77-95.
    3. Jean Barthélemy & Magali Marx, 2012. "Solving Rational Expectations Models," Sciences Po publications info:hdl:2441/3ug0u3qte39, Sciences Po.
    4. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    5. Holden, Thomas, 2016. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130142, ZBW - German National Library of Economics.

    More about this item

    Keywords

    Perturbation methods; monetary policy; indeterminacy; regime switching; DSGE.;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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