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Polynomial Chaos Expansion: Efficient Evaluation and Estimation of Computational Models

Author

Listed:
  • Daniel Fehrle

    (Kiel University)

  • Christopher Heiberger

    (University of Augsburg)

  • Johannes Huber

    (University of Regensburg)

Abstract

We apply Polynomial chaos expansion (PCE) to surrogate time-consuming repeated model evaluations for different parameter values. PCE represents a random variable, the quantity of interest (QoI), as a series expansion of other random variables, the inputs. Repeated evaluations become inexpensive by treating uncertain parameters of a model as inputs, and an element of a model’s solution, e.g., the policy function, second moments, or the posterior kernel as the QoI. We introduce the theory of PCE and apply it to the standard real business cycle model as an illustrative example. We analyze the convergence behavior of PCE for different QoIs and its efficiency when used for estimation. The results are promising both for local and global solution methods.

Suggested Citation

  • Daniel Fehrle & Christopher Heiberger & Johannes Huber, 2025. "Polynomial Chaos Expansion: Efficient Evaluation and Estimation of Computational Models," Computational Economics, Springer;Society for Computational Economics, vol. 65(2), pages 1083-1146, February.
    • Handle: RePEc:kap:compec:v:65:y:2025:i:2:d:10.1007_s10614-024-10772-5
    DOI: 10.1007/s10614-024-10772-5
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    Keywords

    Polynomial chaos expansion; Parameter inference; Parameter uncertainty; Solution methods;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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