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A Generalized Approach to Indeterminacy in Linear Rational Expectations Models

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Abstract

We propose a novel approach to deal with the problem of indeterminacy in Linear Rational Expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard packages without restricting the estimates to the determinacy region. We apply our method to estimate the New-Keynesian model with rational bubbles by Gal (2017) over the period 1982:Q4 until 2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

Suggested Citation

  • Francesco Bianchi & Giovanni Nicolo, 2019. "A Generalized Approach to Indeterminacy in Linear Rational Expectations Models," Finance and Economics Discussion Series 2019-033, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2019-33
    DOI: 10.17016/FEDS.2019.033
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    More about this item

    Keywords

    Bayesian methods; General Equilibrium; Indeterminacy; solution methods;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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