IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2003-61.html
   My bibliography  Save this paper

Calculating and using second order accurate solutions of discrete time dynamic equilibrium models

Author

Listed:
  • Jinill Kim
  • Sunghyun Henry Kim
  • Ernst Schaumburg
  • Christopher A. Sims

Abstract

We describe an algorithm for calculating second order approximations to the solutions to nonlinear stochastic rational expectation models. The paper also explains methods for using such an approximate solution to generate forecasts, simulated time paths for the model, and evaluations of expected welfare differences across different versions of a model. The paper gives conditions for local validity of the approximation that allow for disturbance distributions with unbounded support and allow for non-stationarity of the solution process.

Suggested Citation

  • Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2003-61
    as

    Download full text from publisher

    File URL: http://www.federalreserve.gov/pubs/feds/2003/200361/200361abs.html
    Download Restriction: no

    File URL: http://www.federalreserve.gov/pubs/feds/2003/200361/200361pap.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sutherland, Alan, 2002. "A Simple Second-Order Solution Method For Dynamic General Equilibrium Models," CEPR Discussion Papers 3554, C.E.P.R. Discussion Papers.
    2. 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.
    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. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    5. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 45-75, January.
    6. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, vol. 2(1), pages 1-53, February.
    7. Paul R. Bergin & Ivan Tchakarov, 2003. "Does Exchange Rate Risk Matter for Welfare?," NBER Working Papers 9900, National Bureau of Economic Research, Inc.
    8. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Interest-Rate Rules: I. General Theory," Levine's Bibliography 506439000000000384, UCLA Department of Economics.
    9. 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.
    10. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
    11. 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.
    12. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361, National Bureau of Economic Research, Inc.
    13. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    14. 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.
    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. 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.
    2. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    3. 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.
    4. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    5. 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.
    6. Jinill Kim & Sunghyun Kim, 2018. "Conditional Versus Unconditional Utility as Welfare Criterion: Two Examples," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 719-730, March.
    7. Ozge Senay, 2008. "Interest Rate Rules And Welfare In Open Economies," Scottish Journal of Political Economy, Scottish Economic Society, vol. 55(3), pages 300-329, July.
    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. Ellison, Martin, 2006. "The learning cost of interest rate reversals," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1895-1907, November.
    10. Kollmann, Robert, 2002. "Monetary Policy Rules in a Two-Country World," MPRA Paper 70347, University Library of Munich, Germany.
    11. Pierpaolo Benigno & Michael Woodford, 2005. "Inflation Stabilization And Welfare: The Case Of A Distorted Steady State," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1185-1236, December.
    12. Pierpaolo Benigno & Michael Woodford, 2004. "Optimal Monetary and Fiscal Policy: A Linear-Quadratic Approach," NBER Chapters, in: NBER Macroeconomics Annual 2003, Volume 18, pages 271-364, National Bureau of Economic Research, Inc.
    13. Divino, Jose Angelo, 2009. "Optimal monetary policy for a small open economy," Economic Modelling, Elsevier, vol. 26(2), pages 352-358, March.
    14. De Paoli, Bianca, 2009. "Monetary policy and welfare in a small open economy," Journal of International Economics, Elsevier, vol. 77(1), pages 11-22, February.
    15. Gnocchi, Stefano, 2006. "Optimal simple monetary policy rules and non-atomistic wage setters in a New-Keynesian framework," Working Paper Series 690, European Central Bank.
    16. Pelin Ilbas, 2006. "Optimal Monetary Policy rules for the Euro area in a DSGE framework," Working Papers of Department of Economics, Leuven ces0613, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    17. Pierpaolo Benigno & Michael Woodford, 2007. "Optimal Inflation Targeting under Alternative Fiscal Regimes," Central Banking, Analysis, and Economic Policies Book Series, in: Frederic S. Miskin & Klaus Schmidt-Hebbel & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Se (ed.),Monetary Policy under Inflation Targeting, edition 1, volume 11, chapter 3, pages 037-075, Central Bank of Chile.
    18. Horvath Michal, 2011. "Alternative Perspectives on Optimal Public Debt Adjustment," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-22, November.
    19. Tatiana Damjanovic & Vladislav Damjanovic & Charles Nolan, 2015. "Ordering Policy Rules with an Unconditional Welfare Measure," International Journal of Central Banking, International Journal of Central Banking, vol. 11(1), pages 103-149, January.
    20. Bennett T. McCallum & Edward Nelson, 2004. "Timeless perspective vs. discretionary monetary policy in forward-looking models," Review, Federal Reserve Bank of St. Louis, vol. 86(Mar), pages 43-56.

    More about this item

    Keywords

    Econometric models; Monetary policy;

    JEL classification:

    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:fip:fedgfe:2003-61. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.