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

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/81006/1/MPRA_paper_81006.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "Can we Identify the Fed's Preferences?," EconStor Preprints 149993, ZBW - German National Library of Economics.
    5. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, March.
    6. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy," EconStor Preprints 158001, ZBW - German National Library of Economics.
    7. 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.
    8. Chatelain, Jean-Bernard & Ralf Kirsten, 2016. "Countercyclical versus Procyclical Taylor Principles," EconStor Preprints 129796, ZBW - German National Library of Economics.
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    Cited by:

    1. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "Can we Identify the Fed's Preferences?," EconStor Preprints 149993, ZBW - German National Library of Economics.

    More about this item

    Keywords

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

    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

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