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Fifth-order perturbation solution to DSGE models

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  • Levintal, Oren

Abstract

This paper derives a fifth-order perturbation solution to DSGE models. The paper develops a new notation that reduces the notational complexity of high-order solutions and yields a faster code. The new notation consists of new matrix forms of high-order multivariate chain rules and a new representation of the model as a function of one vector variable. The algorithm that implements the new notation is between 3 and 55 times faster than Dynare++, depending on model size and solution order.

Suggested Citation

  • Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    • Handle: RePEc:eee:dyncon:v:80:y:2017:i:c:p:1-16
    DOI: 10.1016/j.jedc.2017.04.007
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    Cited by:

    1. Sherwin Lott, 2018. "Perturbations in DSGE Models: Odd Derivatives Theorem," PIER Working Paper Archive 18-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 21 May 2018.
    2. Jesús Fernández‐Villaverde & Oren Levintal, 2018. "Solution methods for models with rare disasters," Quantitative Economics, Econometric Society, vol. 9(2), pages 903-944, July.
    3. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    4. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana, 2020. "Uncertainty Shocks and Business Cycle Research," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 118-166, August.
    5. Iania, Leonardo & Tretiakov, Pavel & Wouters, Rafael, 2023. "The risk premium in New Keynesian DSGE models: The cost of inflation channel," Journal of Economic Dynamics and Control, Elsevier, vol. 155(C).
    6. Martin M. Andreasen & Giovanni Caggiano & Efrem Castelnuovo & Giovanni Pellegrino, 2021. "Why Does Risk Matter More in Recessions than in Expansions?," Monash Economics Working Papers 2021-11, Monash University, Department of Economics.
    7. Andreasen, Martin M. & Jørgensen, Kasper, 2020. "The Importance of Timing Attitudes in Consumption-Based Asset Pricing Models," Journal of Monetary Economics, Elsevier, vol. 111(C), pages 95-117.
    8. Farmer, Roger, 2016. "Pricing Assets in an Economy with Two Types of People," CEPR Discussion Papers 11253, C.E.P.R. Discussion Papers.
    9. Kuester, Keith & Jung, Philip & Ignaszak, Marek, 2020. "Federal unemployment reinsurance and local labor-market policies," CEPR Discussion Papers 15465, C.E.P.R. Discussion Papers.
    10. Carlo A. Favero & Fulvio Ortu & Andrea Tamoni & Haoxi Yang, 2020. "Implications of Return Predictability for Consumption Dynamics and Asset Pricing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 527-541, July.
    11. Roger E. A. Farmer, 2018. "Pricing Assets in a Perpetual Youth Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 30, pages 106-124, October.
    12. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Modelling and Estimating Large Macroeconomic Shocks During the Pandemic," CREATES Research Papers 2021-08, Department of Economics and Business Economics, Aarhus University.
    13. Martin M. Andreasen & Giovanni Caggiano & Efrem Castelnuovo & Giovanni Pellegrino, 2021. "Why Does Risk Matter More in Recessions than in Expansions?," "Marco Fanno" Working Papers 0275, Dipartimento di Scienze Economiche "Marco Fanno".
    14. Parra-Alvarez, Juan Carlos & Polattimur, Hamza & Posch, Olaf, 2021. "Risk matters: Breaking certainty equivalence in linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    15. Ruge-Murcia, Francisco, 2020. "Estimating nonlinear dynamic equilibrium models by matching impulse responses," Economics Letters, Elsevier, vol. 197(C).
    16. Juan Carlos Parra-Alvarez & Hamza Polattimur & Olaf Posch, 2020. "Risk Matters: Breaking Certainty Equivalence," CREATES Research Papers 2020-02, Department of Economics and Business Economics, Aarhus University.
    17. Lott, Sherwin, 2019. "Perturbations in DSGE models: An odd derivatives theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    18. Martin M. Andreasen & Anders Kronborg, 2017. "The Extended Perturbation Method: New Insights on the New Keynesian Model," CREATES Research Papers 2017-14, Department of Economics and Business Economics, Aarhus University.
    19. repec:zbw:bofrdp:2021_013 is not listed on IDEAS
    20. Farmer, Roger & Farmer, Leland, 2022. "Zoomers and Boomers: Asset Prices and Intergenerational Inequality," CEPR Discussion Papers 17594, C.E.P.R. Discussion Papers.
    21. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Identifying Economic Shocks in a Rare Disaster Environment," CEIS Research Paper 517, Tor Vergata University, CEIS, revised 19 Nov 2021.
    22. Dennis, Richard, 2022. "Computing time-consistent equilibria: A perturbation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    23. Martin M. Andreasen, 2019. "Explaining Bond Return Predictability in an Estimated New Keynesian Model," CREATES Research Papers 2019-11, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Perturbation; Fifth order; Rare disasters; High-order multivariate chain rules; DSGE;
    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
    • E0 - Macroeconomics and Monetary Economics - - General

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