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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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    3. 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.
    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. 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.
    6. repec:spo:wpmain:info:hdl:2441/3ug0u3qte39q7rqvbmij9rb993 is not listed on IDEAS
    7. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," Working Papers hal-03461113, HAL.

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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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