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State-Dependent Probability Distributions in Non Linear Rational Expectations Models

Author

Listed:
  • Jean Barthélemy

    (Centre de recherche de la Banque de France - Banque de France)

  • Magali Marx

    (Centre de recherche de la Banque de France - Banque de France)

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 diffcult 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

  • Jean Barthélemy & Magali Marx, 2011. "State-Dependent Probability Distributions in Non Linear Rational Expectations Models," Working Papers hal-03461407, HAL.
    • Handle: RePEc:hal:wpaper:hal-03461407
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03461407
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tom D. Holden, 2023. "Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints," The Review of Economics and Statistics, MIT Press, vol. 105(6), pages 1481-1499, November.
    2. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers Main hal-03461113, HAL.
    3. 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.
    4. repec:hal:spmain:info:hdl:2441/3ug0u3qte39q7rqvbmij9rb993 is not listed on IDEAS
    5. 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.
    6. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    7. Jean Barthélemy & Magali Marx, 2012. "Solving Rational Expectations Models," Sciences Po publications info:hdl:2441/3ug0u3qte39, Sciences Po.
    8. Alberto Ortiz-Bolaños & Sebastián Cadavid-Sánchez & Gerardo Kattan-Rodríguez, 2018. "Targeting Long-term Rates in a Model with Financial Frictions and Regime Switching," Investigación Conjunta-Joint Research, in: Alberto Ortiz-Bolaños (ed.), Monetary Policy and Financial Stability in Latin America and the Caribbean, edition 1, volume 1, chapter 6, pages 159-219, Centro de Estudios Monetarios Latinoamericanos, CEMLA.

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    More about this item

    Keywords

    Perturbation Methods; Monetary Policy; Indeterminancy; Regime Switching; DGSE;
    All these keywords.

    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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