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Solving the multi-country real business cycle model using a perturbation method

Author

Listed:
  • Robert Kollmann
  • Jinill Kim

    (Division of Monetary Affairs - Division of Monetary Affairs)

  • Sunghyun H. Kim

    (Department of Economics - Suffolk University)

Abstract

This paper solves the multi-country RBC model described in den Haan, Judd and Juillard (2010) and Juillard and Villemot (2010), 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

  • Robert Kollmann & Jinill Kim & Sunghyun H. Kim, 2010. "Solving the multi-country real business cycle model using a perturbation method," Post-Print hal-00765826, HAL.
    • Handle: RePEc:hal:journl:hal-00765826
    DOI: 10.1016/j.jedc.2010.09.012
    Note: View the original document on HAL open archive server: https://hal.science/hal-00765826
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    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

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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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. 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.
    11. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    12. 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.
    13. 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.
    14. 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.
    15. repec:hum:wpaper:sfb649dp2012-015 is not listed on IDEAS

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    More about this item

    Keywords

    C6; First- and second-order perturbation method; Real business cycle model;
    All these keywords.

    JEL classification:

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

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