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Linear-Quadratic Approximation, Efficiency and Target-Implementability

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Author Info
Paul Levine (University of Surrey)
Joseph Pearlman (London Metropolitan University)
Richard Pierse (University of Surrey)

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Abstract

We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policy

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 441.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:441

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Keywords: Linear-quadratic approximation dynamic stochastic general equilibrium models utility-based loss function

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Find related papers by JEL classification:
E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation
E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lars E O Svensson, 2005. "Monetary Policy with Judgment: Forecast Targeting," International Journal of Central Banking, International Journal of Central Banking, vol. 1(1), May. [Downloadable!]
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  2. Michael Woodford, 2001. "Inflation Stabilization and Welfare," NBER Working Papers 8071, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Richard Clarida & Jordi Gali & Mark Gertler, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December. [Downloadable!] (restricted)
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  4. Jon Faust & Lars E.O. Svensson, 1998. "Transparency and credibility: monetary policy with unobservable goals," International Finance Discussion Papers 605, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  5. Batini, Nicoletta & Justiniano, Alejandro & Levine, Paul & Pearlman, Joseph, 2006. "Robust inflation-forecast-based rules to shield against indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1491-1526. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
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  7. Richard Clarida & Jordi Gali & Mark Gertler, 2002. "A Simple Framework for International Monetary Policy Analysis," NBER Working Papers 8870, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
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  10. Pierpaolo Benigno & Michael Woodford, 2003. "Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach," NBER Working Papers 9905, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Frank Smets & Rafael Wouters, 2002. "An estimated stochastic dynamic general equilibrium model of the euro area," Working Paper Series 171, European Central Bank. [Downloadable!]
  12. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January. [Downloadable!] (restricted)
  13. Petra M. Geraats, 2002. "Central Bank Transparency," Economic Journal, Royal Economic Society, vol. 112(483), pages 532-565, November. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Paul Levine & Peter McAdam & Joseph Pearlman, 2007. "Quantifying and sustaining welfare gains from monetary commitment," Working Paper Series 709, European Central Bank. [Downloadable!]
  2. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers 5964, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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