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Linear-Quadratic Approximation, Efficiency and Target-Implementability

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  • Paul Levine

    (University of Surrey)

  • Joseph Pearlman

    (London Metropolitan University)

  • Richard Pierse

    (University of Surrey)

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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Bibliographic Info

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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References

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  1. Nicoletta Batini & Alejandro Justiniano & Paul Levine & Joseph Pearlman, 2004. "Robust Inflation-Forecast-Based Rules to Shield against Indeterminacy," School of Economics Discussion Papers 0804, School of Economics, University of Surrey.
  2. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, vol. 2(1), pages 1-53, February.
  3. Lars E.O. Svensson, 2005. "Monetary Policy with Judgment: Forecast Targeting," NBER Working Papers 11167, National Bureau of Economic Research, Inc.
  4. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
  5. Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001 3, Society for Computational Economics.
  6. Benigno, Pierpaolo & Woodford, Michael, 2004. "Optimal monetary and fiscal policy: a linear-quadratic approach," Working Paper Series 0345, European Central Bank.
  7. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
  8. Clarida, Richard & Galí, Jordi & Gertler, Mark, 2002. "A Simple Framework for International Monetary Policy Analysis," CEPR Discussion Papers 3355, C.E.P.R. Discussion Papers.
  9. Smets, Frank & Wouters, Raf, 2002. "An estimated stochastic dynamic general equilibrium model of the euro area," Working Paper Series 0171, European Central Bank.
  10. Faust, Jon & Svensson, Lars E O, 2001. "Transparency and Credibility: Monetary Policy with Unobservable Goals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 369-97, May.
  11. Currie,David & Levine,Paul, 1993. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521441964.
  12. Petra M. Geraats, 2002. "Central Bank Transparency," Economic Journal, Royal Economic Society, vol. 112(483), pages 532-565, November.
  13. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," CEPR Discussion Papers 1908, C.E.P.R. Discussion Papers.
  14. Michael Woodford & Pierpaolo Benigno, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," 2004 Meeting Papers 481, Society for Economic Dynamics.
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Cited by:
  1. Levine, Paul & McAdam, Peter & Pearlman, Joseph G., 2007. "Quantifying and sustaining welfare gains from monetary commitment," Working Paper Series 0709, European Central Bank.
  2. Batini, Nicoletta & Gabriel, Vasco & Levine, Paul, 2010. "A Floating versus managed exchange rate regime in a DSGE model of India," Working Papers 10/70, National Institute of Public Finance and Policy.
  3. Batini, Nicoletta & Levine, Paul & Lotti, Emanuela & Yang, Bo, 2011. "Monetary and Fiscal Policy in the Presence of Informal Labour Markets," Working Papers 11/97, National Institute of Public Finance and Policy.
  4. Pierpaolo Benigno & Michael Woodford, 2008. "Linear-Quadratic Approximation of Optimal Policy Problems," Discussion Papers 0809-01, Columbia University, Department of Economics.
  5. Nicoletta Batini & Paul Levine & Emanuela Lotti & Bo Yang, 2011. "Informality, Frictions and Monetary Policy," School of Economics Discussion Papers 0711, School of Economics, University of Surrey.
  6. Paul Levine & Joseph Pearlman & Nicoletta Batini, 2009. "Monetary and Fiscal Rules in an Emerging Small Open Economy," IMF Working Papers 09/22, International Monetary Fund.
  7. Levine, Paul & Pearlman, Joseph, 2011. "Monetary and Fiscal Policy in a DSGE Model of India," Working Papers 11/96, National Institute of Public Finance and Policy.
  8. Paul Levine & Joseph Pearlman & Bo Yang, 2012. "Imperfect Information, Optimal Monetary Policy and Informational Consistency," School of Economics Discussion Papers 1012, School of Economics, University of Surrey.

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