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Solving Stochastic OLG Models Using Chebyshev Parameterized Expectations

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Abstract

This paper presents an efficient solution method for solving stochastic overlapping generations (S-OLG) models. We use the Chebyshev parameterized expectation algorithm (C-PEA) developed by Christiano and Fisher (2000) to solve the life cycle block of S-OLGs. The method is well suited for this family of models, capable of handling nonlinearities inherent in the life-cycle aspect of S-OLGSs, and occasionally binding constraints associated with borrowing constraints. We carefully examine practical considerations and describe how to efficiently implement this method. To illustrate the method’s effectiveness, we apply it to solve a standard S-OLG model with idiosyncratic risk and two permanent types. We calculate Euler equation errors throughout the life cycle and measure computational time to demonstrate that C-PEA can perform well under these computational challenges with reasonable accuracy and efficiency. Our results show that, together with its scalability to higher dimensional problems, C-PEA can be a valuable tool for policy analysts and researchers working with S-OLG models.

Suggested Citation

  • Murat Özbilgin & Robert Kirkby, 2024. "Solving Stochastic OLG Models Using Chebyshev Parameterized Expectations," Treasury Working Paper Series 24/03, New Zealand Treasury.
  • Handle: RePEc:nzt:nztwps:24/03
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    File URL: https://www.treasury.govt.nz/sites/default/files/2024-06/twp24-03.pdf
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    More about this item

    Keywords

    Chebyshev interpolation; Parameterized expectations; Overlapping generations models;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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