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Polynomial chaos expansion: Efficient evaluation and estimation of computational models

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  • Daniel Fehrle
  • Christopher Heiberger
  • Johannes Huber

Abstract

Polynomial chaos expansion (PCE) provides a method that enables the user to represent a quantity of interest (QoI) of a model’s solution as a series expansion of uncertain model inputs, usually its parameters. Among the QoIs are the policy function, the second moments of observables, or the posterior kernel. Hence, PCE sidesteps the repeated and time consuming evaluations of the model’s outcomes. The paper discusses the suitability of PCE for computational economics. We, therefore, introducetothetheorybehindPCE, analyzetheconvergencebehaviorfordifferent elements of the solution of the standard real business cycle model as illustrative example, and check the accuracy, if standard empirical methods are applied. The results are promising, both in terms of accuracy and efï¬ ciency.

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  • Daniel Fehrle & Christopher Heiberger & Johannes Huber, 2020. "Polynomial chaos expansion: Efficient evaluation and estimation of computational models," Working Papers 202, Bavarian Graduate Program in Economics (BGPE).
    • Handle: RePEc:bav:wpaper:202_fehrleheibergerhuber
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    References listed on IDEAS

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    1. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    2. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    3. Burkhard Heer & Alfred Maußner, 2024. "Dynamic General Equilibrium Modeling," Springer Texts in Business and Economics, Springer, edition 3, number 978-3-031-51681-8, October.
    4. Daniel Harenberg & Stefano Marelli & Bruno Sudret & Viktor Winschel, 2019. "Uncertainty quantification and global sensitivity analysis for economic models," Quantitative Economics, Econometric Society, vol. 10(1), pages 1-41, January.
    5. Edward P. Herbst & Frank Schorfheide, 2016. "Bayesian Estimation of DSGE Models," Economics Books, Princeton University Press, edition 1, number 10612.
    6. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    7. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    8. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    9. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
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    More about this item

    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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