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Linear-Quadratic Approximation, Efficiency and Target-Implementability

  • Paul Levine

    (University of Surrey)

  • Joseph Pearlman

    (London Metropolitan University)

  • Richard Pierse

    (University of Surrey)

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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  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. Michael Woodford, 2001. "Inflation Stabilization and Welfare," NBER Working Papers 8071, National Bureau of Economic Research, Inc.
  3. Svensson, Lars E O, 2005. "Monetary Policy with Judgement: Forecast Targeting," CEPR Discussion Papers 5072, C.E.P.R. Discussion Papers.
  4. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "The science of monetary policy: A new Keynesian perspective," Economics Working Papers 356, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 1999.
  5. Pierpaolo Benigno & Michael Woodford, 2003. "Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach," NBER Working Papers 9905, National Bureau of Economic Research, Inc.
  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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Smets, Frank & Wouters, Raf, 2002. "An estimated stochastic dynamic general equilibrium model of the euro area," Working Paper Series 0171, European Central Bank.
  12. repec:cup:cbooks:9780521104609 is not listed on IDEAS
  13. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
  14. Petra M. Geraats, 2002. "Central Bank Transparency," Economic Journal, Royal Economic Society, vol. 112(483), pages 532-565, November.
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