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Polynomial chaos expansion: Efficient evaluation and estimation of computational models

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Polynomial chaos expansion (PCE) provides a method that enables the user to representa quantity of interest (QoI) of a model's solution as a series expansion of uncertainmodel inputs, usually its parameters. Among the QoIs are the policy function,the second moments of observables, or the posterior kernel. Hence, PCE sidesteps therepeated and time consuming evaluations of the model's outcomes.The paper discusses the suitability of PCE for computational economics. We, therefore,introduce to the theory behind PCE, analyze the convergence behavior for differentelements of the solution of the standard real business cycle model as illustrativeexample, and check the accuracy, if standard empirical methods are applied. Theresults are promising, both in terms of accuracy and efficiency.

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  • Daniel Fehrle & Christopher Heiberger & Johannes Huber, 2020. "Polynomial chaos expansion: Efficient evaluation and estimation of computational models," Discussion Paper Series 341, Universitaet Augsburg, Institute for Economics.
    • Handle: RePEc:aug:augsbe:0341
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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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