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

Author

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  • Jean-Bernard Chatelain

    (Paris School of Economics, Université Paris I Pantheon Sorbonne, 48 Boulevard Jourdan, 75014 Paris.)

  • Kirsten Ralf

    (ESCE International Business School, INSEEC U. Research Center, 10 rue Sextius Michel, 75015 Paris)

Abstract

This article presents an algorithm that extends Ljungqvist and Sargent's (2012) dynamic Stackelberg game to the case of dynamic stochastic general equilibrium models including forcing variables. Its first step is the solution of the discounted augmented linear quadratic regulator as in Hansen and Sargent (2007). It then computes the optimal initial anchor of "jump" variables such as inflation. We demonstrate that it is of no use to compute non-observable Lagrange multipliers for all periods in order to obtain impulse response functions and welfare. The algorithm presented, however, enables the computation of a history-dependent representation of a Ramsey policy rule that can be implemented by policy makers and estimated within a vector auto-regressive model. The policy instruments depend on the lagged values of the policy instruments and of the private sector's predetermined and "jump" variables. The algorithm is applied on the new-Keynesian Phillips curve as a monetary policy transmission mechanism.

Suggested Citation

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-18-00579
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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.
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    4. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    5. 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.
    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. Chatelain, Jean-Bernard & Ralf Kirsten, 2016. "Countercyclical versus Procyclical Taylor Principles," EconStor Preprints 129796, ZBW - Leibniz Information Centre for Economics.
    8. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 40(1), pages 140-147.
    9. Chatelain, Jean-Bernard & Ralf, Kirsten, 2021. "Hopf Bifurcation From New-Keynesian Taylor Rule To Ramsey Optimal Policy," Macroeconomic Dynamics, Cambridge University Press, vol. 25(8), pages 2204-2236, December.
    10. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, April.
    11. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
    12. 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.
    13. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    14. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "The Indeterminacy of Determinacy with Fiscal, Macro-prudential or Taylor Rules," PSE Working Papers halshs-01877766, HAL.
    2. 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.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," Working Papers halshs-01863367, HAL.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    5. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Persistence-Dependent Optimal Policy Rules," PSE Working Papers halshs-02919697, HAL.
    6. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    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. Chatelain, Jean-Bernard & Ralf, Kirsten, 2021. "Hopf Bifurcation From New-Keynesian Taylor Rule To Ramsey Optimal Policy," Macroeconomic Dynamics, Cambridge University Press, vol. 25(8), pages 2204-2236, December.
    9. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 40(2), pages 1797-1803.
    10. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 40(1), pages 140-147.
    11. Jean-Bernard Chatelain & Kirsten Ralf, 2023. "Super-Inertial Interest Rate Rules are not Solutions of Ramsey Optimal Policy," Revue d'économie politique, Dalloz, vol. 133(1), pages 119-146.

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    More about this item

    Keywords

    Ramsey optimal policy; Stackelberg dynamic game; algorithm; forcing variables; augmented linear quadratic regulator; new-Keynesian Phillips curve.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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