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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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    Cited by:

    1. Jean Barthélemy & Magali Marx, 2012. "Solving Rational Expectations Models," Sciences Po publications info:hdl:2441/3ug0u3qte39, Sciences Po.
    2. 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.
    3. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers Main hal-03461113, HAL.
    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. repec:hal:spmain:info:hdl:2441/3ug0u3qte39q7rqvbmij9rb993 is not listed on IDEAS
    6. 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.
    7. 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.
    8. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS

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    More about this item

    Keywords

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