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Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach

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  • Ajevskis, Viktors

Abstract

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and the fact that the solutions to general equilibrium models converge to a steady state. Under certain nonlocal conditions, the convergence of the approximate solutions to the true solution is proved. We also show that the proposed approach can be treated as a rigorous proof of convergence for the extended path algorithm in a class of nonlinear rational expectation models.

Suggested Citation

  • Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    • Handle: RePEc:cup:macdyn:v:23:y:2019:i:06:p:2544-2571_00
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    Cited by:

    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.

    More about this item

    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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