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Non-Local Solutions to Dynamic Equilibrium Models: the Approximate Stable Manifolds Approach

Author

Listed:
  • Viktors Ajevskis

    (Bank of Latvia)

Abstract
This paper presents a method to construct a sequence of approximate policy functions of increasing accuracy on non-local domains. The method is based upon the notion of stable manifold originated from dynamical systems theory. The approximate policy functions are constructed employing the contraction mapping theorem and the fact that solutions to rational expectations models converge to a steady state. The approach allows us to derive the accuracy of the approximations and their domain of definition. The method is applied to the neoclassical growth model and compared with the perturbation method. Just the second approximation of the proposed approach yields very high accuracy of the approximate solution on a global domain. In contrast to the Taylor series expansions, the solutions of the method inherit globally the properties of the true solution such as monotonicity and concavity.

Suggested Citation

  • Viktors Ajevskis, 2013. "Non-Local Solutions to Dynamic Equilibrium Models: the Approximate Stable Manifolds Approach," Working Papers 2013/03, Latvijas Banka.
    • Handle: RePEc:ltv:wpaper:201303
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    1. Montes-Galdón, Carlos & Ajevskis, Viktors & Brázdik, František & Garcia, Pablo & Gatt, William & Lima, Diana & Mavromatis, Kostas & Ortega, Eva & Papadopoulou, Niki & De Lorenzo, Ivan & Kolb, Benedikt, 2024. "Using structural models to understand macroeconomic tail risks," Occasional Paper Series 357, European Central Bank.

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    More about this item

    Keywords

    dynamic equilibrium; rational expectations; non-linear perfect foresight models; stable manifold; perturbation method; extended path; neoclassical growth model;
    All these keywords.

    JEL classification:

    • 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
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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