IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i4p604-615.html
   My bibliography  Save this article

Second-order approximation of dynamic models without the use of tensors

Author

Listed:
  • Gomme, Paul
  • Klein, Paul

Abstract

Several approaches to finding the second-order approximation to a dynamic model have been proposed recently. This paper differs from the existing literature in that it makes use of the Magnus and Neudecker (1999) definition of the Hessian matrix. The key result is a linear system of equations that characterizes the second-order coefficients. No use is made of multi-dimensional arrays or tensors, a practical implication of which is that it is much easier to transcribe the mathematical representation of the solution into usable computer code. Matlab code is available from http://paulklein.se/newsite/codes/codes.php; Fortran 90 code is available from http://alcor.concordia.ca/~pgomme/.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:4:p:604-615
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00234-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Lombardo, Giovanni & Sutherland, Alan, 2007. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 515-530, February.
    3. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
    4. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    5. King, Robert G & Watson, Mark W, 2002. "System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 57-86, October.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    7. OndŘej KamenÍk, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 167-187, February.
    8. 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.
    9. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
    10. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
    11. 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.
    12. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
    13. 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.
    14. Unknown, 2001. "General Discussion," Proceedings of the 6th Agricultural and Food Policy Systems Information Workshop, 2000: Trade Liberalization Under NAFTA: Report Card on Agriculture 16839, Farm Foundation, Agricultural and Food Policy Systems Information Workshops.
    15. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    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. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," EconStor Preprints 269876, ZBW - Leibniz Information Centre for Economics.
    2. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," MPRA Paper 116480, University Library of Munich, Germany.
    3. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    4. 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.
    5. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    6. Lombardo, Giovanni & Sutherland, Alan, 2007. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 515-530, February.
    7. Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Solving DSGE models with perturbation methods and a change of variables," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2509-2531, December.
    8. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2003. "Some results on the solution of the neoclassical growth model," FRB Atlanta Working Paper 2003-34, Federal Reserve Bank of Atlanta.
    9. 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.
    10. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    11. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    12. 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.
    13. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2167-2185.
    14. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.
    15. 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.
    16. Ajevskis Viktors, 2017. "Semi-global solutions to DSGE models: perturbation around a deterministic path," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-28, April.
    17. Francesco Bianchi & Giovanni Nicolò, 2021. "A generalized approach to indeterminacy in linear rational expectations models," Quantitative Economics, Econometric Society, vol. 12(3), pages 843-868, July.
    18. Viktors Ajevskis, 2019. "Generalised Impulse Response Function as a Perturbation of a Global Solution to DSGE Models," Working Papers 2019/04, Latvijas Banka.
    19. Ajevskis, Viktors, 2014. "Global Solutions to DSGE Models as a Perturbation of a Deterministic Path," MPRA Paper 55145, University Library of Munich, Germany.
    20. repec:hal:spmain:info:hdl:2441/3ug0u3qte39q7rqvbmij9rb993 is not listed on IDEAS
    21. Michel Juillard & Tarik Ocaktan, 2008. "Méthodes de simulation des modèles stochastiques d'équilibre général," Economie & Prévision, La Documentation Française, vol. 0(2), pages 115-126.

    More about this item

    Keywords

    Solving dynamic models Second-order approximation;

    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:eee:dyncon:v:35:y:2011:i:4:p:604-615. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.