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Scalable Global Solution Techniques for High-Dimensional Models in Dynare

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Listed:
  • Aryan Eftekhari
  • Michel Juillard
  • Normann Rion
  • Simon Scheidegger

Abstract

For over three decades, Dynare has been a cornerstone of dynamic stochastic modeling in economics, relying primarily on perturbation-based local solution methods. However, these techniques often falter in high-dimensional, non-linear models that demand more comprehensive approaches. This paper demonstrates that global solutions of economic models with substantial heterogeneity and frictions can be computed accurately and swiftly by augmenting Dynare with adaptive sparse grids (SGs) and high-dimensional model representation (HDMR). SGs mitigate the curse of dimensionality, as the number of grid points grows significantly slower than in traditional tensor-product Cartesian grids. Additionally, adaptivity focuses grid refinement on regions with steep gradients or non-differentiabilities, enhancing computational efficiency. Complementing SGs, HDMR tackles large state spaces by approximating policy functions with a hierarchical expansion of low-dimensional terms. Using a time iteration algorithm, we benchmark our approach on an international real business cycle model. Our results show that both SGs and HDMR alleviate the curse of dimensionality, enabling accurate solutions for at least 100-dimensional models on standard hardware in relatively short times. This advancement extends Dynare's capabilities beyond perturbation approaches, establishing a versatile platform for sophisticated non-linear models and paving the way for integrating the most recent global solution methods, such as those from machine learning.

Suggested Citation

  • Aryan Eftekhari & Michel Juillard & Normann Rion & Simon Scheidegger, 2025. "Scalable Global Solution Techniques for High-Dimensional Models in Dynare," Papers 2503.11464, arXiv.org.
  • Handle: RePEc:arx:papers:2503.11464
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    1. Yongyang Cai & Thomas S. Lontzek, 2019. "The Social Cost of Carbon with Economic and Climate Risks," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2684-2734.
    2. Duffy, John & McNelis, Paul D., 2001. "Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1273-1303, September.
    3. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 182-204.
    4. Kollmann, Robert & Maliar, Serguei & Malin, Benjamin A. & Pichler, Paul, 2011. "Comparison of solutions to the multi-country Real Business Cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 186-202, February.
    5. Adjemian, Stéphane & Juillard, Michel & Karamé, Fréderic & Mutschler, Willi & Pfeifer, Johannes & Ratto, Marco & Rion, Normann & Villemot, Sébastien, 2024. "Dynare: Reference Manual, Version 6," Dynare Working Papers 80, CEPREMAP, revised Feb 2025.
    6. Andriy Norets, 2012. "Estimation of Dynamic Discrete Choice Models Using Artificial Neural Network Approximations," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 84-106.
    7. Juillard, Michel & Villemot, Sébastien, 2011. "Multi-country real business cycle models: Accuracy tests and test bench," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 178-185, February.
    8. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    9. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    10. Dirk Krueger & Felix Kubler, 2006. "Pareto-Improving Social Security Reform when Financial Markets are Incomplete!?," American Economic Review, American Economic Association, vol. 96(3), pages 737-755, June.
    11. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    12. Viktor Winschel & Markus Kr‰tzig, 2010. "Solving, Estimating, and Selecting Nonlinear Dynamic Models Without the Curse of Dimensionality," Econometrica, Econometric Society, vol. 78(2), pages 803-821, March.
    13. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
    14. Laurence Kotlikoff & Felix Kubler & Andrey Polbin & Simon Scheidegger, 2021. "Pareto-improving carbon-risk taxation [The environment and directed technical change]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 36(107), pages 551-589.
    15. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    16. Vytautas Valaitis & Alessandro T. Villa, 2024. "A machine learning projection method for macro‐finance models," Quantitative Economics, Econometric Society, vol. 15(1), pages 145-173, January.
    17. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2023. "Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 91(3), pages 869-901, May.
    18. Marlon Azinovic & Luca Gaegauf & Simon Scheidegger, 2022. "Deep Equilibrium Nets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1471-1525, November.
    19. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
    20. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
    21. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.
    22. Luca Gaegauf & Simon Scheidegger & Fabio Trojani, 2023. "A Comprehensive Machine Learning Framework for Dynamic Portfolio Choice With Transaction Costs," Swiss Finance Institute Research Paper Series 23-114, Swiss Finance Institute.
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