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Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions

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  • Maliar, Lilia
  • Maliar, Serguei
  • Villemot, Sébastien

Abstract

Local (perturbation) methods compute solutions in one point and tend to deliver far lower accuracy levels than global solution methods. We develop a hybrid method that solves for some policy functions locally (using a perturbation method) and that solves for the other policy functions globally (using closed-form expressions and a numerical solver). We applied our hybrid method to solve large-scale RBC models used in the comparison analysis of Kollmann et al. (J Econ Dyn Control 35:186–202, 2011b). We obtain more accurate solutions than those produced by any other (either local or global) solution method participating in that comparison. Our running time is a few seconds.

Suggested Citation

  • Maliar, Lilia & Maliar, Serguei & Villemot, Sébastien, 2011. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Dynare Working Papers 6, CEPREMAP, revised Jul 2012.
    • Handle: RePEc:cpm:dynare:006
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    1. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    2. Maliar, Serguei & Maliar, Lilia & Judd, Kenneth, 2011. "Solving the multi-country real business cycle model using ergodic set methods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 207-228, February.
    3. Collard, Fabrice & Juillard, Michel, 2001. "A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model," Computational Economics, Springer;Society for Computational Economics, vol. 17(2-3), pages 125-139, June.
    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. 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.
    6. Kollmann, Robert & Kim, Jinill & Kim, Sunghyun H., 2011. "Solving the multi-country Real Business Cycle model using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 203-206, February.
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    9. Malin, Benjamin A. & Krueger, Dirk & Kubler, Felix, 2011. "Solving the multi-country real business cycle model using a Smolyak-collocation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 229-239, February.
    10. Lilia Maliar & Serguei Maliar, 2003. "The Representative Consumer in the Neoclassical Growth Model with Idiosyncratic Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(2), pages 368-380, April.
    11. Chen, Baoline & Zadrozny, Peter A., 2009. "Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2061-2074, April.
    12. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, July.
    13. Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Inna Tsener, 2017. "How to solve dynamic stochastic models computing expectations just once," Quantitative Economics, Econometric Society, vol. 8(3), pages 851-893, November.
    14. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
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    16. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
    17. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 240-251, February.
    18. Dotsey, Michael & Mao, Ching Sheng, 1992. "How well do linear approximation methods work? : The production tax case," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 25-58, February.
    19. Gary S. Anderson & Andrew T. Levin & Eric T. Swanson, 2006. "Higher-order perturbation solutions to dynamic, discrete-time rational expectations models," Working Paper Series 2006-01, Federal Reserve Bank of San Francisco.
    20. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    21. Adjemian, Stéphane & Bastani, Houtan & Juillard, Michel & Karamé, Fréderic & Maih, Junior & Mihoubi, Ferhat & Mutschler, Willi & Perendia, George & Pfeifer, Johannes & Ratto, Marco & Villemot, Sébasti, 2011. "Dynare: Reference Manual Version 4," Dynare Working Papers 1, CEPREMAP, revised Mar 2021.
    22. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
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    Citations

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    Cited by:

    1. Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.
    2. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    3. Lepetyuk, Vadym & Maliar, Lilia & Maliar, Serguei, 2020. "When the U.S. catches a cold, Canada sneezes: A lower-bound tale told by deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    4. Hänsel, Matthias, 2024. "Solving the Diamond–Mortensen–Pissarides model: A hybrid perturbation approach," Economics Letters, Elsevier, vol. 236(C).
    5. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2017. "Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models," Econometrica, Econometric Society, vol. 85, pages 991-1012, May.
    6. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    7. Vadym Lepetyuk & Lilia Maliar & Serguei Maliar, 2017. "Should Central Banks Worry About Nonlinearities of their Large-Scale Macroeconomic Models?," Staff Working Papers 17-21, Bank of Canada.
    8. Balcilar, Mehmet & Gupta, Rangan & Kotzé, Kevin, 2015. "Forecasting macroeconomic data for an emerging market with a nonlinear DSGE model," Economic Modelling, Elsevier, vol. 44(C), pages 215-228.

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    More about this item

    Keywords

    Dynare; Perturbation; Hybrid; Accuracy; Numerical methods; Approximation;
    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
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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