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On the Solution of Markov-switching Rational Expectations Models

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  • Carravetta, Francesco
  • Sorge, Marco M.

Abstract

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.

Suggested Citation

  • Carravetta, Francesco & Sorge, Marco M., 2011. "On the Solution of Markov-switching Rational Expectations Models," Bonn Econ Discussion Papers 05/2011, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:052011
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    More about this item

    Keywords

    Rational Expectations; Markov-switching dynamic systems; Dynamic programming; Time-varying Kalman filter;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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