IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/81006.html
   My bibliography  Save this paper

A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables

Author

Listed:
  • Chatelain, Jean-Bernard
  • Ralf, Kirsten

Abstract

This algorithm extends Ljungqvist and Sargent (2012) algorithm of Stackelberg dynamic game to the case of dynamic stochastic general equilibrium models including exogenous forcing variables. It is based Anderson, Hansen, McGrattan, Sargent (1996) discounted augmented linear quadratic regulator. It adds an intermediate step in solving a Sylvester equation. Forward-looking variables are also optimally anchored on forcing variables. This simple algorithm calls for already programmed routines for Ricatti, Sylvester and Inverse matrix in Matlab and Scilab. A final step using a change of basis vector computes a vector auto regressive representation including Ramsey optimal policy rule function of lagged observable variables, when the exogenous forcing variables are not observable.

Suggested Citation

  • Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," MPRA Paper 81006, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:81006
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/81006/1/MPRA_paper_81006.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 140-147.
    2. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252, Elsevier.
    3. Miller, Marcus & Salmon, Mark, 1985. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," Economic Journal, Royal Economic Society, vol. 95(380a), pages 124-137, Supplemen.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    5. Amman, Hans, 1996. "Numerical methods for linear-quadratic models," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 13, pages 587-618, Elsevier.
    6. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    7. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, September.
    8. Taylor, John B., 1999. "The robustness and efficiency of monetary policy rules as guidelines for interest rate setting by the European central bank," Journal of Monetary Economics, Elsevier, vol. 43(3), pages 655-679, June.
    9. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    10. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    11. Chatelain, Jean-Bernard & Ralf Kirsten, 2016. "Countercyclical versus Procyclical Taylor Principles," EconStor Preprints 129796, ZBW - Leibniz Information Centre for Economics.
    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. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Imperfect Credibility versus No Credibility of Optimal Monetary Policy," Revue économique, Presses de Sciences-Po, vol. 72(1), pages 43-63.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions," Economics Bulletin, AccessEcon, vol. 40(1), pages 140-147.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 1797-1803.
    5. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Policy Maker’s Credibility with Predetermined Instruments for Forward-Looking Targets," Revue d'économie politique, Dalloz, vol. 130(5), pages 823-846.
    6. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    7. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "Ramsey Optimal Policy in the New-Keynesian Model with Public Debt," PSE Working Papers halshs-02278781, HAL.
    8. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "The Indeterminacy of Determinacy with Fiscal, Macro-prudential or Taylor Rules," Working Papers halshs-01877766, HAL.
    9. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," PSE Working Papers halshs-01863367, HAL.
    10. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Persistence-Dependent Optimal Policy Rules," PSE Working Papers halshs-02919697, HAL.

    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. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 1797-1803.
    4. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "How macroeconomists lost control of stabilization policy: towards dark ages," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 27(6), pages 938-982, November.
    5. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "The Indeterminacy of Determinacy with Fiscal, Macro-prudential or Taylor Rules," Working Papers halshs-01877766, HAL.
    6. Chatelain, Jean-Bernard & Ralf, Kirsten, 2014. "Stability and Identification with Optimal Macroprudential Policy Rules," EconStor Preprints 95979, ZBW - Leibniz Information Centre for Economics.
    7. Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Imperfect Credibility versus No Credibility of Optimal Monetary Policy," Revue économique, Presses de Sciences-Po, vol. 72(1), pages 43-63.
    8. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," PSE Working Papers halshs-01863367, HAL.
    9. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    10. Ricardo Nunes & Jinill Kim & Jesper Linde & Davide Debortoli, 2014. "Designing a Simple Loss Function for the Fed: Does the Dual Mandate Make Sense?," 2014 Meeting Papers 1043, Society for Economic Dynamics.
    11. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    12. Chatelain, Jean-Bernard & Ralf Kirsten, 2016. "Countercyclical versus Procyclical Taylor Principles," EconStor Preprints 129796, ZBW - Leibniz Information Centre for Economics.
    13. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "Ramsey Optimal Policy in the New-Keynesian Model with Public Debt," PSE Working Papers halshs-02278781, HAL.
    14. Cristiano Cantore & Vasco J. Gabriel & Paul Levine & Joseph Pearlman & Bo Yang, 2013. "The science and art of DSGE modelling: II – model comparisons, model validation, policy analysis and general discussion," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 19, pages 441-463, Edward Elgar Publishing.
    15. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
    16. Richard Dennis & Tatiana Kirsanova, 2010. "Expectations traps and coordination failures: selecting among multiple discretionary equilibria," Working Paper Series 2010-02, Federal Reserve Bank of San Francisco.
    17. Davide Debortoli & Jinill Kim & Jesper Lindé & Ricardo Nunes, 2019. "Designing a Simple Loss Function for Central Banks: Does a Dual Mandate Make Sense?," Economic Journal, Royal Economic Society, vol. 129(621), pages 2010-2038.
    18. Dario Caldara & Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Wen Yao, 2012. "Computing DSGE Models with Recursive Preferences and Stochastic Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 188-206, April.
    19. Dario Caldara & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez & Wen Yao, 2009. "Computing DSGE Models with Recursive Preferences," PIER Working Paper Archive 09-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.

    More about this item

    Keywords

    Ramsey optimal policy; Stackelberg dynamic game; algorithm; forcing variables; augmented linear quadratic regulator.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy

    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:pra:mprapa:81006. 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: (Joachim Winter). General contact details of provider: https://edirc.repec.org/data/vfmunde.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 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.

    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.