IDEAS home Printed from https://ideas.repec.org/p/zbw/imfswp/302176.html
   My bibliography  Save this paper

Solving and analyzing DSGE models in the frequency domain

Author

Listed:
  • Meyer-Gohde, Alexander

Abstract

I provide a solution method in the frequency domain for multivariate linear rational expectations models. The method works with the generalized Schur decomposition, providing a numerical implementation of the underlying analytic function solution methods suitable for standard DSGE estimation and analysis procedures. This approach generalizes the time-domain restriction of autoregressive-moving average exogenous driving forces to arbitrary covariance stationary processes. Applied to the standard New Keynesian model, I find that a Bayesian analysis favors a single parameter log harmonic function of the lag operator over the usual AR(1) assumption as it generates humped shaped autocorrelation patterns more consistent with the data.

Suggested Citation

  • Meyer-Gohde, Alexander, 2024. "Solving and analyzing DSGE models in the frequency domain," IMFS Working Paper Series 207, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    • Handle: RePEc:zbw:imfswp:302176
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/302176/1/190063323X.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-1026, November.
    2. Han, Zhao & Tan, Fei & Wu, Jieran, 2022. "Analytic policy function iteration," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    4. Christoph Görtz & John D. Tsoukalas & Francesco Zanetti, 2022. "News Shocks under Financial Frictions," American Economic Journal: Macroeconomics, American Economic Association, vol. 14(4), pages 210-243, October.
    5. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and uniqueness of perturbation solutions to DSGE models," SFB 649 Discussion Papers 2012-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Martins, Manuel M.F. & Verona, Fabio, 2023. "Inflation dynamics in the frequency domain," Economics Letters, Elsevier, vol. 231(C).
    7. Futia, Carl A, 1981. "Rational Expectations in Stationary Linear Models," Econometrica, Econometric Society, vol. 49(1), pages 171-192, January.
    8. 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.
    9. Tan, Fei & Walker, Todd B., 2015. "Solving generalized multivariate linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 95-111.
    10. Kenneth Kasa, 2000. "Forecasting the Forecasts of Others in the Frequency Domain," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 726-756, October.
    11. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
    12. Tan, Fei, 2021. "A Frequency-Domain Approach To Dynamic Macroeconomic Models," Macroeconomic Dynamics, Cambridge University Press, vol. 25(6), pages 1381-1411, September.
    13. Luca Sala, 2015. "Dsge Models in the Frequency Domains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 219-240, March.
    14. Dück, Alexander & Verona, Fabio, 2023. "Robust frequency-based monetary policy rules," IMFS Working Paper Series 180, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    15. Onatski, Alexei, 2006. "Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 323-345, February.
    16. Eric M. Leeper & Todd B. Walker & Shu‐Chun Susan Yang, 2013. "Fiscal Foresight and Information Flows," Econometrica, Econometric Society, vol. 81(3), pages 1115-1145, May.
    17. Meyer-Gohde, Alexander, 2010. "Linear rational-expectations models with lagged expectations: A synthetic method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 984-1002, May.
    18. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    19. Meyer-Gohde, Alexander & Tzaawa-Krenzler, Mary, 2023. "Sticky information and the Taylor principle," IMFS Working Paper Series 189, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    20. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-118, May.
    21. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    22. 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.
    23. Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP.
    24. Meyer-Gohde, Alexander & Neuhoff, Daniel, 2015. "Solving and estimating linearized DSGE models with VARMA shock processes and filtered data," Economics Letters, Elsevier, vol. 133(C), pages 89-91.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meyer-Gohde, Alexander & Tzaawa-Krenzler, Mary, 2023. "Sticky information and the Taylor principle," IMFS Working Paper Series 189, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    2. Tan, Fei & Walker, Todd B., 2015. "Solving generalized multivariate linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 95-111.
    3. Tan, Fei, 2018. "A Frequency-Domain Approach to Dynamic Macroeconomic Models," MPRA Paper 90487, University Library of Munich, Germany.
    4. Rondina, Giacomo & Walker, Todd B., 2021. "Confounding dynamics," Journal of Economic Theory, Elsevier, vol. 196(C).
    5. Meyer-Gohde, Alexander & Neuhoff, Daniel, 2015. "Generalized exogenous processes in DSGE: A Bayesian approach," SFB 649 Discussion Papers 2015-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Paul Levine & Joseph Pearlman & Stephen Wright & Bo Yang, 2023. "Imperfect Information and Hidden Dynamics," School of Economics Discussion Papers 1223, School of Economics, University of Surrey.
    7. Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    8. Schmidt, Sebastian & Wieland, Volker, 2013. "The New Keynesian Approach to Dynamic General Equilibrium Modeling: Models, Methods and Macroeconomic Policy Evaluation," Handbook of Computable General Equilibrium Modeling, in: Peter B. Dixon & Dale Jorgenson (ed.), Handbook of Computable General Equilibrium Modeling, edition 1, volume 1, chapter 0, pages 1439-1512, Elsevier.
    9. Meyer-Gohde, Alexander, 2023. "Numerical stability analysis of linear DSGE models: Backward errors, forward errors and condition numbers," IMFS Working Paper Series 193, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    10. 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.
    11. Meyer-Gohde, Alexander, 2021. "On the accuracy of linear DSGE solution methods and the consequences for log-normal asset pricing," IMFS Working Paper Series 154, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    12. Jurado, Kyle, 2023. "Rational inattention in the frequency domain," Journal of Economic Theory, Elsevier, vol. 208(C).
    13. Kenneth Kasa, 2000. "Forecasting the Forecasts of Others in the Frequency Domain," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 726-756, October.
    14. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.
    15. Francesco Carravetta & Marco Sorge, 2010. "A “Nearly Ideal” Solution to Linear Time-Varying Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 331-353, April.
    16. Walker, Todd B., 2007. "How equilibrium prices reveal information in a time series model with disparately informed, competitive traders," Journal of Economic Theory, Elsevier, vol. 137(1), pages 512-537, November.
    17. 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.
    18. Cho, Seonghoon & McCallum, Bennett T., 2015. "Refining linear rational expectations models and equilibria," Journal of Macroeconomics, Elsevier, vol. 46(C), pages 160-169.
    19. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    20. Anna Mikusheva, 2014. "Estimation of dynamic stochastic general equilibrium models (in Russian)," Quantile, Quantile, issue 12, pages 1-21, February.

    More about this item

    Keywords

    DSGE; solution methods; spectral methods; Bayesian estimation; general exogenous processes;
    All these keywords.

    JEL classification:

    • 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
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:imfswp:302176. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/hoffmde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.