IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i2p203-206.html
   My bibliography  Save this article

Solving the multi-country Real Business Cycle model using a perturbation method

Author

Listed:
  • Kollmann, Robert
  • Kim, Jinill
  • Kim, Sunghyun H.

Abstract

This paper solves the multi-country RBC model described in den Haan et al. (this issue) and Juillard and Villemot (this issue), using a perturbation method. We explain how to apply first- and second-order versions of the gensys2.m algorithm to this model. The perturbation method is computationally cheap and can easily be applied to large models with possibly hundreds of state variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:2:p:203-206
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00216-2
    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. 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.
    2. 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.
    3. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
    4. Jinill Kim & Sunghyun Kim, 2018. "Welfare Effects of Tax Policy in Open Economies: Stabilization and Cooperation," International Journal of Central Banking, International Journal of Central Banking, vol. 14(3), pages 347-376, June.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    6. Kollmann, Robert, 2008. "Welfare-Maximizing Operational Monetary And Tax Policy Rules," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S1), pages 112-125, April.
    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. Kim, Sunghyun Henry & Kollmann, Robert & Kim, Jinill, 2010. "Solving the incomplete market model with aggregate uncertainty using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 50-58, January.
    9. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2011. "Computational suite of models with heterogeneous agents II: Multi-country real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 175-177, February.
    10. Massimiliano Marzo & Thomas A. Lubik, 2004. "Monetary Policy, Fiscal Policy and Automatic Stabilizers: Welfare and Macroeconomic Stability," Computing in Economics and Finance 2004 170, Society for Computational Economics.
    11. Paul R. Bergin & Hyung-Cheol Shin & Ivan Tchakarov, 2017. "Does Exchange Rate Variability Matter for Welfare? A Quantitative Investigation of Stabilization Policies," World Scientific Book Chapters, in: International Macroeconomic Interdependence, chapter 13, pages 363-386, World Scientific Publishing Co. Pte. Ltd..
    12. 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.
    13. Robert Kollmann, 2004. "Welfare Effects of a Monetary Union: The Role of Trade Openness," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 289-301, 04/05.
    14. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers.
    15. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 989-1015, July.
    16. 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.
    17. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Robert Kollmann, 2015. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 239-260, February.
    3. 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.
    4. Chase Coleman & Spencer Lyon & Lilia Maliar & Serguei Maliar, 2021. "Matlab, Python, Julia: What to Choose in Economics?," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1263-1288, December.
    5. Kollmann, Robert, 2020. "Rational Bubbles in Non-Linear Business Cycle Models: Closed and Open Economies," CEPR Discussion Papers 14367, C.E.P.R. Discussion Papers.
    6. Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 307-325, October.
    7. Kollmann, Robert, 2013. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation," CEPR Discussion Papers 9469, C.E.P.R. Discussion Papers.
    8. 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.
    9. 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.
    10. Hong Lan & Alexander Meyer-Gohde, 2012. "Existence and Uniqueness of Perturbation Solutions to DSGE Models," SFB 649 Discussion Papers SFB649DP2012-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2011. "Computational suite of models with heterogeneous agents II: Multi-country real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 175-177, February.
    12. 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.
    13. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    14. Robert Kollmann, 2013. "Estimation of non-linear DSGE models made easy: taking second-order model approximations to the data (with an application to a DSGE model with a banking sector)," 2013 Meeting Papers 1255, Society for Economic Dynamics.

    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. Francisco (F.) Blasques & Marc Nientker, 2019. "Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium Models," Tinbergen Institute Discussion Papers 19-012/III, Tinbergen Institute, revised 09 Feb 2020.
    2. Paolo Zagaglia, 2007. "Operational Fiscal and Monetary Policy with Staggered Wage and Price Dynamics," Finnish Economic Papers, Finnish Economic Association, vol. 20(2), pages 121-138, Autumn.
    3. Moldovan, Ioana R., 2010. "Countercyclical taxes in a monopolistically competitive environment," European Economic Review, Elsevier, vol. 54(5), pages 692-717, July.
    4. Elekdag, Selim & Tchakarov, Ivan, 2007. "Balance sheets, exchange rate policy, and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3986-4015, December.
    5. Marattin, Luigi & Marzo, Massimiliano & Zagaglia, Paolo, 2013. "Distortionary tax instruments and implementable monetary policy," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 219-243.
    6. Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 307-325, October.
    7. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    8. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    9. 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.
    10. Faia, Ester & Monacelli, Tommaso, 2007. "Optimal interest rate rules, asset prices, and credit frictions," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3228-3254, October.
    11. Faia, Ester, 2009. "Ramsey monetary policy with labor market frictions," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 570-581, May.
    12. Yongyang Cai & Kenneth Judd & Jevgenijs Steinbuks, 2017. "A nonlinear certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 8(1), pages 117-147, March.
    13. 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.
    14. Lambertini, Luisa & Mendicino, Caterina & Teresa Punzi, Maria, 2013. "Leaning against boom–bust cycles in credit and housing prices," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1500-1522.
    15. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," MPRA Paper 116480, University Library of Munich, Germany.
    16. 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.
    17. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    18. Robert Kollmann, 2013. "Tractable latent state filtering for non-linear DSGE models using a second-order Approximation," CAMA Working Papers 2013-29, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    19. Moldovan, Ioana R., 2008. "Countercyclical Fiscal Policy and Cyclical Factor Utilization," SIRE Discussion Papers 2008-19, Scottish Institute for Research in Economics (SIRE).
    20. 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.

    More about this item

    Keywords

    First- and second-order perturbation method Real Business Cycle model;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    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:2:p:203-206. 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.