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The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks

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  • Jean-Bernard Chatelain

    (PJSE)

  • Kirsten Ralf

Abstract

With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock. JEL classification numbers: C61, C62, C73, E47, E52, E61, E63.

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," Papers 2006.14842, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14842
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    References listed on IDEAS

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    1. 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.
    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, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    4. 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.
    5. 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.
    6. 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.
    7. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," Working Papers halshs-01863367, HAL.
    8. 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.
    9. 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.
    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.
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Persistence-Dependent Optimal Policy Rules," PSE Working Papers halshs-02919697, 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, 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

    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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